@testset "3.2.2 (f+g x)^m (h+i x)^q (A+B log(e ((a+b x) over (c+d x))^n))^p" begin
    (A, B, a, b, c, d, e, f, g, h, i, m, n, p, x, ) = @variables A B a b c d e f g h i m n p x

    #= ::Package:: =#

    #= ::Title:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*((a+b*x)/(c+d*x))^n))^p=#


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*((a+b*x)/(c+d*x))^n))^p*when*b*f-a*g=0*and*d*h-c*i=0=#


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*(a+b*x) / (c+d*x)))^1*when*b*f-a*g=0*and*d*h-c*i=0=#


    #= ::Subsubsection::Closed:: =#
    #=q>0=#


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x))), x, 5, -((B*(b*c - a*d)^4*g^3*i*x)/(20*b*d^3)) + (B*(b*c - a*d)^3*g^3*i*(a + b*x)^2)/(40*b^2*d^2) - (B*(b*c - a*d)^2*g^3*i*(a + b*x)^3)/(60*b^2*d) + (g^3*i*(a + b*x)^4*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*b) + ((b*c - a*d)*g^3*i*(a + b*x)^4*(A - B + B*log((e*(a + b*x))/(c + d*x))))/(20*b^2) + (B*(b*c - a*d)^5*g^3*i*log(c + d*x))/(20*b^2*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x))), x, 5, (B*(b*c - a*d)^3*g^2*i*x)/(12*b*d^2) - (B*(b*c - a*d)^2*g^2*i*(a + b*x)^2)/(24*b^2*d) + (g^2*i*(a + b*x)^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*b) + ((b*c - a*d)*g^2*i*(a + b*x)^3*(A - B + B*log((e*(a + b*x))/(c + d*x))))/(12*b^2) - (B*(b*c - a*d)^4*g^2*i*log(c + d*x))/(12*b^2*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x))), x, 5, -((B*(b*c - a*d)^2*g*i*x)/(6*b*d)) + (g*i*(a + b*x)^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*b) + ((b*c - a*d)*g*i*(a + b*x)^2*(A - B + B*log((e*(a + b*x))/(c + d*x))))/(6*b^2) + (B*(b*c - a*d)^3*g*i*log(c + d*x))/(6*b^2*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x))), x, 4, -((B*(b*c - a*d)*i*x)/(2*b)) - (B*(b*c - a*d)^2*i*log(a + b*x))/(2*b^2*d) + (i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*d)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^1, x, 6, (i*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b*g) - ((b*c - a*d)*i*log(-((b*c - a*d)/(d*(a + b*x))))*(A - B + B*log((e*(a + b*x))/(c + d*x))))/(b^2*g) + (B*(b*c - a*d)*i*PolyLog(2, 1 + (b*c - a*d)/(d*(a + b*x))))/(b^2*g)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^2, x, 5, -((B*i*(c + d*x))/(b*g^2*(a + b*x))) - (i*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b*g^2*(a + b*x)) - (d*i*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2) + (B*d*i*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^3, x, 2, -((B*i*(c + d*x)^2)/(4*(b*c - a*d)*g^3*(a + b*x)^2)) - (i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)*g^3*(a + b*x)^2)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^4, x, 5, (B*d*i*(c + d*x)^2)/(4*(b*c - a*d)^2*g^4*(a + b*x)^2) - (b*B*i*(c + d*x)^3)/(9*(b*c - a*d)^2*g^4*(a + b*x)^3) + (d*i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^2*g^4*(a + b*x)^2) - (b*i*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*(b*c - a*d)^2*g^4*(a + b*x)^3)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^5, x, 5, -((B*d^2*i*(c + d*x)^2)/(4*(b*c - a*d)^3*g^5*(a + b*x)^2)) + (2*b*B*d*i*(c + d*x)^3)/(9*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*B*i*(c + d*x)^4)/(16*(b*c - a*d)^3*g^5*(a + b*x)^4) - (d^2*i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^3*g^5*(a + b*x)^2) + (2*b*d*i*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*i*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*(b*c - a*d)^3*g^5*(a + b*x)^4)]


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x))), x, 5, (B*(b*c - a*d)^5*g^3*i^2*x)/(60*b^2*d^3) + (B*(b*c - a*d)^4*g^3*i^2*(c + d*x)^2)/(120*b*d^4) - (19*B*(b*c - a*d)^3*g^3*i^2*(c + d*x)^3)/(180*d^4) + (13*b*B*(b*c - a*d)^2*g^3*i^2*(c + d*x)^4)/(120*d^4) - (b^2*B*(b*c - a*d)*g^3*i^2*(c + d*x)^5)/(30*d^4) + (B*(b*c - a*d)^6*g^3*i^2*log((a + b*x)/(c + d*x)))/(60*b^3*d^4) - ((b*c - a*d)^3*g^3*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*d^4) + (3*b*(b*c - a*d)^2*g^3*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*d^4) - (3*b^2*(b*c - a*d)*g^3*i^2*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*d^4) + (b^3*g^3*i^2*(c + d*x)^6*(A + B*log((e*(a + b*x))/(c + d*x))))/(6*d^4) + (B*(b*c - a*d)^6*g^3*i^2*log(c + d*x))/(60*b^3*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x))), x, 5, -((B*(b*c - a*d)^4*g^2*i^2*x)/(30*b^2*d^2)) - (B*(b*c - a*d)^3*g^2*i^2*(c + d*x)^2)/(60*b*d^3) + (B*(b*c - a*d)^2*g^2*i^2*(c + d*x)^3)/(10*d^3) - (b*B*(b*c - a*d)*g^2*i^2*(c + d*x)^4)/(20*d^3) - (B*(b*c - a*d)^5*g^2*i^2*log((a + b*x)/(c + d*x)))/(30*b^3*d^3) + ((b*c - a*d)^2*g^2*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*d^3) - (b*(b*c - a*d)*g^2*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*d^3) + (b^2*g^2*i^2*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*d^3) - (B*(b*c - a*d)^5*g^2*i^2*log(c + d*x))/(30*b^3*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x))), x, 5, (B*(b*c - a*d)^3*g*i^2*x)/(12*b^2*d) + (B*(b*c - a*d)^2*g*i^2*(c + d*x)^2)/(24*b*d^2) - (B*(b*c - a*d)*g*i^2*(c + d*x)^3)/(12*d^2) + (B*(b*c - a*d)^4*g*i^2*log((a + b*x)/(c + d*x)))/(12*b^3*d^2) - ((b*c - a*d)*g*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*d^2) + (b*g*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*d^2) + (B*(b*c - a*d)^4*g*i^2*log(c + d*x))/(12*b^3*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x))), x, 4, -((B*(b*c - a*d)^2*i^2*x)/(3*b^2)) - (B*(b*c - a*d)*i^2*(c + d*x)^2)/(6*b*d) - (B*(b*c - a*d)^3*i^2*log(a + b*x))/(3*b^3*d) + (i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*d)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^1, x, 10, -((B*d*(b*c - a*d)*i^2*x)/(2*b^2*g)) - (B*(b*c - a*d)^2*i^2*log((a + b*x)/(c + d*x)))/(2*b^3*g) + (d*(b*c - a*d)*i^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g) + (i^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*b*g) - (3*B*(b*c - a*d)^2*i^2*log(c + d*x))/(2*b^3*g) - ((b*c - a*d)^2*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) + (B*(b*c - a*d)^2*i^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^2, x, 8, -((B*(b*c - a*d)*i^2*(c + d*x))/(b^2*g^2*(a + b*x))) + (d^2*i^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g^2) - ((b*c - a*d)*i^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^2*g^2*(a + b*x)) - (B*d*(b*c - a*d)*i^2*log(c + d*x))/(b^3*g^2) - (2*d*(b*c - a*d)*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2) + (2*B*d*(b*c - a*d)*i^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^3, x, 7, -((B*d*i^2*(c + d*x))/(b^2*g^3*(a + b*x))) - (B*i^2*(c + d*x)^2)/(4*b*g^3*(a + b*x)^2) - (d*i^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^2*g^3*(a + b*x)) - (i^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*b*g^3*(a + b*x)^2) - (d^2*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3) + (B*d^2*i^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^4, x, 2, -((B*i^2*(c + d*x)^3)/(9*(b*c - a*d)*g^4*(a + b*x)^3)) - (i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*(b*c - a*d)*g^4*(a + b*x)^3)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^5, x, 5, (B*d*i^2*(c + d*x)^3)/(9*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*B*i^2*(c + d*x)^4)/(16*(b*c - a*d)^2*g^5*(a + b*x)^4) + (d*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*(b*c - a*d)^2*g^5*(a + b*x)^4)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^6, x, 5, -((B*d^2*i^2*(c + d*x)^3)/(9*(b*c - a*d)^3*g^6*(a + b*x)^3)) + (b*B*d*i^2*(c + d*x)^4)/(8*(b*c - a*d)^3*g^6*(a + b*x)^4) - (b^2*B*i^2*(c + d*x)^5)/(25*(b*c - a*d)^3*g^6*(a + b*x)^5) - (d^2*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*(b*c - a*d)^3*g^6*(a + b*x)^3) + (b*d*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^3*g^6*(a + b*x)^4) - (b^2*i^2*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*(b*c - a*d)^3*g^6*(a + b*x)^5)]


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x))), x, 5, (B*(b*c - a*d)^6*g^3*i^3*x)/(140*b^3*d^3) + (B*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2)/(280*b^2*d^4) + (B*(b*c - a*d)^4*g^3*i^3*(c + d*x)^3)/(420*b*d^4) - (17*B*(b*c - a*d)^3*g^3*i^3*(c + d*x)^4)/(280*d^4) + (b*B*(b*c - a*d)^2*g^3*i^3*(c + d*x)^5)/(14*d^4) - (b^2*B*(b*c - a*d)*g^3*i^3*(c + d*x)^6)/(42*d^4) + (B*(b*c - a*d)^7*g^3*i^3*log((a + b*x)/(c + d*x)))/(140*b^4*d^4) - ((b*c - a*d)^3*g^3*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*d^4) + (3*b*(b*c - a*d)^2*g^3*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*d^4) - (b^2*(b*c - a*d)*g^3*i^3*(c + d*x)^6*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*d^4) + (b^3*g^3*i^3*(c + d*x)^7*(A + B*log((e*(a + b*x))/(c + d*x))))/(7*d^4) + (B*(b*c - a*d)^7*g^3*i^3*log(c + d*x))/(140*b^4*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x))), x, 5, -((B*(b*c - a*d)^5*g^2*i^3*x)/(60*b^3*d^2)) - (B*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2)/(120*b^2*d^3) - (B*(b*c - a*d)^3*g^2*i^3*(c + d*x)^3)/(180*b*d^3) + (7*B*(b*c - a*d)^2*g^2*i^3*(c + d*x)^4)/(120*d^3) - (b*B*(b*c - a*d)*g^2*i^3*(c + d*x)^5)/(30*d^3) - (B*(b*c - a*d)^6*g^2*i^3*log((a + b*x)/(c + d*x)))/(60*b^4*d^3) + ((b*c - a*d)^2*g^2*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*d^3) - (2*b*(b*c - a*d)*g^2*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*d^3) + (b^2*g^2*i^3*(c + d*x)^6*(A + B*log((e*(a + b*x))/(c + d*x))))/(6*d^3) - (B*(b*c - a*d)^6*g^2*i^3*log(c + d*x))/(60*b^4*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x))), x, 5, (B*(b*c - a*d)^4*g*i^3*x)/(20*b^3*d) + (B*(b*c - a*d)^3*g*i^3*(c + d*x)^2)/(40*b^2*d^2) + (B*(b*c - a*d)^2*g*i^3*(c + d*x)^3)/(60*b*d^2) - (B*(b*c - a*d)*g*i^3*(c + d*x)^4)/(20*d^2) + (B*(b*c - a*d)^5*g*i^3*log((a + b*x)/(c + d*x)))/(20*b^4*d^2) - ((b*c - a*d)*g*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*d^2) + (b*g*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*d^2) + (B*(b*c - a*d)^5*g*i^3*log(c + d*x))/(20*b^4*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x))), x, 4, -((B*(b*c - a*d)^3*i^3*x)/(4*b^3)) - (B*(b*c - a*d)^2*i^3*(c + d*x)^2)/(8*b^2*d) - (B*(b*c - a*d)*i^3*(c + d*x)^3)/(12*b*d) - (B*(b*c - a*d)^4*i^3*log(a + b*x))/(4*b^4*d) + (i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*d)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^1, x, 14, -((5*B*d*(b*c - a*d)^2*i^3*x)/(6*b^3*g)) - (B*(b*c - a*d)*i^3*(c + d*x)^2)/(6*b^2*g) - (5*B*(b*c - a*d)^3*i^3*log((a + b*x)/(c + d*x)))/(6*b^4*g) + (d*(b*c - a*d)^2*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^4*g) + ((b*c - a*d)*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*b^2*g) + (i^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*b*g) - (11*B*(b*c - a*d)^3*i^3*log(c + d*x))/(6*b^4*g) - ((b*c - a*d)^3*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g) + (B*(b*c - a*d)^3*i^3*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^2, x, 11, -((B*d^2*(b*c - a*d)*i^3*x)/(2*b^3*g^2)) - (B*(b*c - a*d)^2*i^3*(c + d*x))/(b^3*g^2*(a + b*x)) - (B*d*(b*c - a*d)^2*i^3*log((a + b*x)/(c + d*x)))/(2*b^4*g^2) + (2*d^2*(b*c - a*d)*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^4*g^2) - ((b*c - a*d)^2*i^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g^2*(a + b*x)) + (d*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*b^2*g^2) - (5*B*d*(b*c - a*d)^2*i^3*log(c + d*x))/(2*b^4*g^2) - (3*d*(b*c - a*d)^2*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) + (3*B*d*(b*c - a*d)^2*i^3*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^3, x, 9, -((2*B*d*(b*c - a*d)*i^3*(c + d*x))/(b^3*g^3*(a + b*x))) - (B*(b*c - a*d)*i^3*(c + d*x)^2)/(4*b^2*g^3*(a + b*x)^2) + (d^3*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^4*g^3) - (2*d*(b*c - a*d)*i^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g^3*(a + b*x)) - ((b*c - a*d)*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*b^2*g^3*(a + b*x)^2) - (B*d^2*(b*c - a*d)*i^3*log(c + d*x))/(b^4*g^3) - (3*d^2*(b*c - a*d)*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3) + (3*B*d^2*(b*c - a*d)*i^3*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^4, x, 9, -((B*d^2*i^3*(c + d*x))/(b^3*g^4*(a + b*x))) - (B*d*i^3*(c + d*x)^2)/(4*b^2*g^4*(a + b*x)^2) - (B*i^3*(c + d*x)^3)/(9*b*g^4*(a + b*x)^3) - (d^2*i^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g^4*(a + b*x)) - (d*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*b^2*g^4*(a + b*x)^2) - (i^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*b*g^4*(a + b*x)^3) - (d^3*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^4) + (B*d^3*i^3*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^4)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^5, x, 2, -((B*i^3*(c + d*x)^4)/(16*(b*c - a*d)*g^5*(a + b*x)^4)) - (i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*(b*c - a*d)*g^5*(a + b*x)^4)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^6, x, 5, (B*d*i^3*(c + d*x)^4)/(16*(b*c - a*d)^2*g^6*(a + b*x)^4) - (b*B*i^3*(c + d*x)^5)/(25*(b*c - a*d)^2*g^6*(a + b*x)^5) + (d*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*(b*c - a*d)^2*g^6*(a + b*x)^4) - (b*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*(b*c - a*d)^2*g^6*(a + b*x)^5)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(a*g + b*g*x)^7, x, 5, -((B*d^2*i^3*(c + d*x)^4)/(16*(b*c - a*d)^3*g^7*(a + b*x)^4)) + (2*b*B*d*i^3*(c + d*x)^5)/(25*(b*c - a*d)^3*g^7*(a + b*x)^5) - (b^2*B*i^3*(c + d*x)^6)/(36*(b*c - a*d)^3*g^7*(a + b*x)^6) - (d^2*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*(b*c - a*d)^3*g^7*(a + b*x)^4) + (2*b*d*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*(b*c - a*d)^3*g^7*(a + b*x)^5) - (b^2*i^3*(c + d*x)^6*(A + B*log((e*(a + b*x))/(c + d*x))))/(6*(b*c - a*d)^3*g^7*(a + b*x)^6)]


    #= ::Subsubsection::Closed:: =#
    #=q<0=#


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x), x, 6, (g^3*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*d*i) - ((b*c - a*d)*g^3*(a + b*x)^2*(3*A + B + 3*B*log((e*(a + b*x))/(c + d*x))))/(6*d^2*i) + ((b*c - a*d)^2*g^3*(a + b*x)*(6*A + 5*B + 6*B*log((e*(a + b*x))/(c + d*x))))/(6*d^3*i) + ((b*c - a*d)^3*g^3*log((b*c - a*d)/(b*(c + d*x)))*(6*A + 11*B + 6*B*log((e*(a + b*x))/(c + d*x))))/(6*d^4*i) + (B*(b*c - a*d)^3*g^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x), x, 5, (g^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*d*i) - ((b*c - a*d)*g^2*(a + b*x)*(2*A + B + 2*B*log((e*(a + b*x))/(c + d*x))))/(2*d^2*i) - ((b*c - a*d)^2*g^2*log((b*c - a*d)/(b*(c + d*x)))*(2*A + 3*B + 2*B*log((e*(a + b*x))/(c + d*x))))/(2*d^3*i) - (B*(b*c - a*d)^2*g^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x), x, 4, (g*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(d*i) + ((b*c - a*d)*g*log((b*c - a*d)/(b*(c + d*x)))*(A + B + B*log((e*(a + b*x))/(c + d*x))))/(d^2*i) + (B*(b*c - a*d)*g*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x), x, 5, -((log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(d*i)) - (B*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d*i)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^1*(c*i + d*i*x)), x, 2, (A + B*log((e*(a + b*x))/(c + d*x)))^2/(2*B*(b*c - a*d)*g*i)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^2*(c*i + d*i*x)), x, 5, -((b*B*(c + d*x))/((b*c - a*d)^2*g^2*i*(a + b*x))) + (B*d*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^2*g^2*i) - (b*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^2*g^2*i*(a + b*x)) - (d*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^2*g^2*i)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^3*(c*i + d*i*x)), x, 7, -((B*(c + d*x)^2*(b - (4*d*(a + b*x))/(c + d*x))^2)/(4*(b*c - a*d)^3*g^3*i*(a + b*x)^2)) - (B*d^2*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^3*g^3*i) + (2*b*d*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^3*g^3*i*(a + b*x)) - (b^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^3*g^3*i*(a + b*x)^2) + (d^2*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^3*g^3*i)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^4*(c*i + d*i*x)), x, 8, -((3*b*B*d^2*(c + d*x))/((b*c - a*d)^4*g^4*i*(a + b*x))) + (3*b^2*B*d*(c + d*x)^2)/(4*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (b^3*B*(c + d*x)^3)/(9*(b*c - a*d)^4*g^4*i*(a + b*x)^3) + (B*d^3*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^4*g^4*i) - (3*b*d^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^4*i*(a + b*x)) + (3*b^2*d*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (b^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*(b*c - a*d)^4*g^4*i*(a + b*x)^3) - (d^3*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^4*i)]


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x)^2, x, 9, (3*B*(b*c - a*d)^2*g^3*(a + b*x))/(d^3*i^2*(c + d*x)) - ((6*A + 5*B)*(b*c - a*d)^2*g^3*(a + b*x))/(2*d^3*i^2*(c + d*x)) - (3*B*(b*c - a*d)^2*g^3*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d^3*i^2*(c + d*x)) + (g^3*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*d*i^2*(c + d*x)) - ((b*c - a*d)*g^3*(a + b*x)^2*(3*A + B + 3*B*log((e*(a + b*x))/(c + d*x))))/(2*d^2*i^2*(c + d*x)) - (b*(b*c - a*d)^2*g^3*log((b*c - a*d)/(b*(c + d*x)))*(6*A + 5*B + 6*B*log((e*(a + b*x))/(c + d*x))))/(2*d^4*i^2) - (3*b*B*(b*c - a*d)^2*g^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^2)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x)^2, x, 8, -((2*B*(b*c - a*d)*g^2*(a + b*x))/(d^2*i^2*(c + d*x))) + ((2*A + B)*(b*c - a*d)*g^2*(a + b*x))/(d^2*i^2*(c + d*x)) + (2*B*(b*c - a*d)*g^2*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d^2*i^2*(c + d*x)) + (g^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(d*i^2*(c + d*x)) + (b*(b*c - a*d)*g^2*log((b*c - a*d)/(b*(c + d*x)))*(2*A + B + 2*B*log((e*(a + b*x))/(c + d*x))))/(d^3*i^2) + (2*b*B*(b*c - a*d)*g^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^2)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x)^2, x, 7, -((A*g*(a + b*x))/(d*i^2*(c + d*x))) + (B*g*(a + b*x))/(d*i^2*(c + d*x)) - (B*g*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d*i^2*(c + d*x)) - (b*g*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^2*i^2) - (b*B*g*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i^2)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x)^2, x, 3, (A*(a + b*x))/((b*c - a*d)*i^2*(c + d*x)) - (B*(a + b*x))/((b*c - a*d)*i^2*(c + d*x)) + (B*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)*i^2*(c + d*x))]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^1*(c*i + d*i*x)^2), x, 5, -((A*d*(a + b*x))/((b*c - a*d)^2*g*i^2*(c + d*x))) + (B*d*(a + b*x))/((b*c - a*d)^2*g*i^2*(c + d*x)) - (B*d*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^2*g*i^2*(c + d*x)) + (b*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*B*(b*c - a*d)^2*g*i^2)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^2*(c*i + d*i*x)^2), x, 4, -((B*d^2*(a + b*x))/((b*c - a*d)^3*g^2*i^2*(c + d*x))) - (b^2*B*(c + d*x))/((b*c - a*d)^3*g^2*i^2*(a + b*x)) + (b*B*d*log((a + b*x)/(c + d*x))^2)/((b*c - a*d)^3*g^2*i^2) + (d^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^3*g^2*i^2*(c + d*x)) - (b^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^3*g^2*i^2*(a + b*x)) - (2*b*d*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^3*g^2*i^2)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^3*(c*i + d*i*x)^2), x, 8, (B*d^3*(a + b*x))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (3*b^2*B*d*(c + d*x))/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*B*(c + d*x)^2)/(4*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) - (3*b*B*d^2*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^4*g^3*i^2) - (d^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (3*b^2*d*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) + (3*b*d^2*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^3*i^2)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^4*(c*i + d*i*x)^2), x, 4, -((B*d^4*(a + b*x))/((b*c - a*d)^5*g^4*i^2*(c + d*x))) - (6*b^2*B*d^2*(c + d*x))/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (b^3*B*d*(c + d*x)^2)/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (b^4*B*(c + d*x)^3)/(9*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) + (2*b*B*d^3*log((a + b*x)/(c + d*x))^2)/((b*c - a*d)^5*g^4*i^2) + (d^4*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^4*i^2*(c + d*x)) - (6*b^2*d^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (2*b^3*d*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (b^4*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) - (4*b*d^3*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^4*i^2)]


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x)^3, x, 9, -((3*B*(b*c - a*d)*g^3*(a + b*x)^2)/(4*d^2*i^3*(c + d*x)^2)) - (3*b*B*(b*c - a*d)*g^3*(a + b*x))/(d^3*i^3*(c + d*x)) + (b*(3*A + B)*(b*c - a*d)*g^3*(a + b*x))/(d^3*i^3*(c + d*x)) + (3*b*B*(b*c - a*d)*g^3*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d^3*i^3*(c + d*x)) + (g^3*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(d*i^3*(c + d*x)^2) + ((b*c - a*d)*g^3*(a + b*x)^2*(3*A + B + 3*B*log((e*(a + b*x))/(c + d*x))))/(2*d^2*i^3*(c + d*x)^2) + (b^2*(b*c - a*d)*g^3*log((b*c - a*d)/(b*(c + d*x)))*(3*A + B + 3*B*log((e*(a + b*x))/(c + d*x))))/(d^4*i^3) + (3*b^2*B*(b*c - a*d)*g^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^3)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x)^3, x, 8, (B*g^2*(a + b*x)^2)/(4*d*i^3*(c + d*x)^2) - (A*b*g^2*(a + b*x))/(d^2*i^3*(c + d*x)) + (b*B*g^2*(a + b*x))/(d^2*i^3*(c + d*x)) - (b*B*g^2*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d^2*i^3*(c + d*x)) - (g^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*d*i^3*(c + d*x)^2) - (b^2*g^2*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^3*i^3) - (b^2*B*g^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^3)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x)^3, x, 2, -((B*g*(a + b*x)^2)/(4*(b*c - a*d)*i^3*(c + d*x)^2)) + (g*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)*i^3*(c + d*x)^2)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*(a + b*x)/(c + d*x)))/(c*i + d*i*x)^3, x, 4, B/(4*d*i^3*(c + d*x)^2) + (b*B)/(2*d*(b*c - a*d)*i^3*(c + d*x)) + (b^2*B*log(a + b*x))/(2*d*(b*c - a*d)^2*i^3) - (A + B*log((e*(a + b*x))/(c + d*x)))/(2*d*i^3*(c + d*x)^2) - (b^2*B*log(c + d*x))/(2*d*(b*c - a*d)^2*i^3)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^1*(c*i + d*i*x)^3), x, 4, -((B*(4*b - (d*(a + b*x))/(c + d*x))^2)/(4*(b*c - a*d)^3*g*i^3)) - (b^2*B*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^3*g*i^3) + (d^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^3*g*i^3*(c + d*x)^2) - (2*b*d*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^3*g*i^3*(c + d*x)) + (b^2*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^3*g*i^3)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^2*(c*i + d*i*x)^3), x, 4, (B*d^3*(a + b*x)^2)/(4*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2) - (3*b*B*d^2*(a + b*x))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) - (b^3*B*(c + d*x))/((b*c - a*d)^4*g^2*i^3*(a + b*x)) + (3*b^2*B*d*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^4*g^2*i^3) - (d^3*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2) + (3*b*d^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) - (b^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^2*i^3*(a + b*x)) - (3*b^2*d*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^2*i^3)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^3*(c*i + d*i*x)^3), x, 5, -((B*d^4*(a + b*x)^2)/(4*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2)) + (4*b*B*d^3*(a + b*x))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) + (4*b^3*B*d*(c + d*x))/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*B*(c + d*x)^2)/(4*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) - (3*b^2*B*d^2*log((a + b*x)/(c + d*x))^2)/((b*c - a*d)^5*g^3*i^3) + (d^4*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2) - (4*b*d^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) + (4*b^3*d*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) + (6*b^2*d^2*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^3*i^3)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))/((a*g + b*g*x)^4*(c*i + d*i*x)^3), x, 8, (B*d^5*(a + b*x)^2)/(4*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2) - (5*b*B*d^4*(a + b*x))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) - (10*b^3*B*d^2*(c + d*x))/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*B*d*(c + d*x)^2)/(4*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (b^5*B*(c + d*x)^3)/(9*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) + (5*b^2*B*d^3*log((a + b*x)/(c + d*x))^2)/((b*c - a*d)^6*g^4*i^3) - (d^5*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2) + (5*b*d^4*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) - (10*b^3*d^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*d*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (b^5*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) - (10*b^2*d^3*log((a + b*x)/(c + d*x))*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^6*g^4*i^3)]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*(a+b*x) / (c+d*x)))^2*when*b*f-a*g=0*and*d*h-c*i=0=#


    #= ::Subsubsection::Closed:: =#
    #=q>0=#


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 11, (3*B^2*(b*c - a*d)^4*g^3*i*x)/(10*b*d^3) - (3*B^2*(b*c - a*d)^3*g^3*i*(c + d*x)^2)/(20*d^4) + (b*B^2*(b*c - a*d)^2*g^3*i*(c + d*x)^3)/(30*d^4) - (B*(b*c - a*d)^2*g^3*i*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(30*b^2*d) - (B*(b*c - a*d)*g^3*i*(a + b*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(10*b^2) + ((b*c - a*d)*g^3*i*(a + b*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(20*b^2) + (g^3*i*(a + b*x)^4*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(5*b) + (B*(b*c - a*d)^3*g^3*i*(a + b*x)^2*(3*A + B + 3*B*log((e*(a + b*x))/(c + d*x))))/(60*b^2*d^2) - (B*(b*c - a*d)^4*g^3*i*(a + b*x)*(6*A + 5*B + 6*B*log((e*(a + b*x))/(c + d*x))))/(60*b^2*d^3) - (B*(b*c - a*d)^5*g^3*i*log((b*c - a*d)/(b*(c + d*x)))*(6*A + 11*B + 6*B*log((e*(a + b*x))/(c + d*x))))/(60*b^2*d^4) - (B^2*(b*c - a*d)^5*g^3*i*log(c + d*x))/(10*b^2*d^4) - (B^2*(b*c - a*d)^5*g^3*i*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(10*b^2*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 10, -((B^2*(b*c - a*d)^3*g^2*i*x)/(3*b*d^2)) + (B^2*(b*c - a*d)^2*g^2*i*(c + d*x)^2)/(12*d^3) - (B*(b*c - a*d)^2*g^2*i*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(12*b^2*d) - (B*(b*c - a*d)*g^2*i*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(6*b^2) + ((b*c - a*d)*g^2*i*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(12*b^2) + (g^2*i*(a + b*x)^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(4*b) + (B*(b*c - a*d)^3*g^2*i*(a + b*x)*(2*A + B + 2*B*log((e*(a + b*x))/(c + d*x))))/(12*b^2*d^2) + (B*(b*c - a*d)^4*g^2*i*log((b*c - a*d)/(b*(c + d*x)))*(2*A + 3*B + 2*B*log((e*(a + b*x))/(c + d*x))))/(12*b^2*d^3) + (B^2*(b*c - a*d)^4*g^2*i*log(c + d*x))/(6*b^2*d^3) + (B^2*(b*c - a*d)^4*g^2*i*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(6*b^2*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 9, (B^2*(b*c - a*d)^2*g*i*x)/(3*b*d) - (B*(b*c - a*d)^2*g*i*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*b^2*d) - (B*(b*c - a*d)*g*i*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*b^2) + ((b*c - a*d)*g*i*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(6*b^2) + (g*i*(a + b*x)^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*b) - (B*(b*c - a*d)^3*g*i*log((b*c - a*d)/(b*(c + d*x)))*(A + B + B*log((e*(a + b*x))/(c + d*x))))/(3*b^2*d^2) - (B^2*(b*c - a*d)^3*g*i*log(c + d*x))/(3*b^2*d^2) - (B^2*(b*c - a*d)^3*g*i*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(3*b^2*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 7, -((B*(b*c - a*d)*i*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/b^2) + (i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*d) + (B^2*(b*c - a*d)^2*i*log(c + d*x))/(b^2*d) + (B*(b*c - a*d)^2*i*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^2*d) - (B^2*(b*c - a*d)^2*i*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^2*d)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^1, x, 8, (2*B*(b*c - a*d)*i*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^2*g) + (d*i*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^2*g) - ((b*c - a*d)*i*(A + B*log((e*(a + b*x))/(c + d*x)))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^2*g) + (2*B^2*(b*c - a*d)*i*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^2*g) + (2*B*(b*c - a*d)*i*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g) + (2*B^2*(b*c - a*d)*i*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^2, x, 7, -((2*B^2*i*(c + d*x))/(b*g^2*(a + b*x))) - (2*B*i*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b*g^2*(a + b*x)) - (i*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b*g^2*(a + b*x)) - (d*i*(A + B*log((e*(a + b*x))/(c + d*x)))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2) + (2*B*d*i*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2) + (2*B^2*d*i*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^3, x, 3, -((B^2*i*(c + d*x)^2)/(4*(b*c - a*d)*g^3*(a + b*x)^2)) - (B*i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)*g^3*(a + b*x)^2) - (i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)*g^3*(a + b*x)^2)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^4, x, 7, (B^2*d*i*(c + d*x)^2)/(4*(b*c - a*d)^2*g^4*(a + b*x)^2) - (2*b*B^2*i*(c + d*x)^3)/(27*(b*c - a*d)^2*g^4*(a + b*x)^3) + (B*d*i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^2*g^4*(a + b*x)^2) - (2*b*B*i*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(9*(b*c - a*d)^2*g^4*(a + b*x)^3) + (d*i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^2*g^4*(a + b*x)^2) - (b*i*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*(b*c - a*d)^2*g^4*(a + b*x)^3)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^5, x, 9, -((B^2*d^2*i*(c + d*x)^2)/(4*(b*c - a*d)^3*g^5*(a + b*x)^2)) + (4*b*B^2*d*i*(c + d*x)^3)/(27*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*B^2*i*(c + d*x)^4)/(32*(b*c - a*d)^3*g^5*(a + b*x)^4) - (B*d^2*i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^3*g^5*(a + b*x)^2) + (4*b*B*d*i*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(9*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*B*i*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(8*(b*c - a*d)^3*g^5*(a + b*x)^4) - (d^2*i*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^3*g^5*(a + b*x)^2) + (2*b*d*i*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*i*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(4*(b*c - a*d)^3*g^5*(a + b*x)^4)]


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 17, (3*B^2*(b*c - a*d)^5*g^3*i^2*x)/(20*b^2*d^3) + (B^2*(b*c - a*d)^2*g^3*i^2*(a + b*x)^4)/(60*b^3) - (3*B^2*(b*c - a*d)^4*g^3*i^2*(c + d*x)^2)/(40*b*d^4) + (B^2*(b*c - a*d)^3*g^3*i^2*(c + d*x)^3)/(60*d^4) - (B*(b*c - a*d)^3*g^3*i^2*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(90*b^3*d) - (B*(b*c - a*d)^2*g^3*i^2*(a + b*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(20*b^3) - (B*(b*c - a*d)*g^3*i^2*(a + b*x)^4*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(15*b^2) + ((b*c - a*d)^2*g^3*i^2*(a + b*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(60*b^3) + ((b*c - a*d)*g^3*i^2*(a + b*x)^4*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(15*b^2) + (g^3*i^2*(a + b*x)^4*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(6*b) + (B*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2*(3*A + B + 3*B*log((e*(a + b*x))/(c + d*x))))/(180*b^3*d^2) - (B*(b*c - a*d)^5*g^3*i^2*(a + b*x)*(6*A + 5*B + 6*B*log((e*(a + b*x))/(c + d*x))))/(180*b^3*d^3) - (B*(b*c - a*d)^6*g^3*i^2*log((b*c - a*d)/(b*(c + d*x)))*(6*A + 11*B + 6*B*log((e*(a + b*x))/(c + d*x))))/(180*b^3*d^4) - (B^2*(b*c - a*d)^6*g^3*i^2*log(c + d*x))/(20*b^3*d^4) - (B^2*(b*c - a*d)^6*g^3*i^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(30*b^3*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 15, -((B^2*(b*c - a*d)^4*g^2*i^2*x)/(10*b^2*d^2)) - (B^2*(b*c - a*d)^3*g^2*i^2*(c + d*x)^2)/(20*b*d^3) + (B^2*(b*c - a*d)^2*g^2*i^2*(c + d*x)^3)/(30*d^3) + (B^2*(b*c - a*d)^5*g^2*i^2*log((a + b*x)/(c + d*x)))/(30*b^3*d^3) - (B*(b*c - a*d)^3*g^2*i^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(30*b^3*d) - (B*(b*c - a*d)^2*g^2*i^2*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(15*b^3) - (B*(b*c - a*d)^3*g^2*i^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(5*b*d^3) + (4*B*(b*c - a*d)^2*g^2*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(15*d^3) - (b*B*(b*c - a*d)*g^2*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(10*d^3) + ((b*c - a*d)^2*g^2*i^2*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(30*b^3) + ((b*c - a*d)*g^2*i^2*(a + b*x)^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(10*b^2) + (g^2*i^2*(a + b*x)^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(5*b) + (B*(b*c - a*d)^4*g^2*i^2*(a + b*x)*(2*A + B + 2*B*log((e*(a + b*x))/(c + d*x))))/(30*b^3*d^2) + (B*(b*c - a*d)^5*g^2*i^2*log((b*c - a*d)/(b*(c + d*x)))*(2*A + 3*B + 2*B*log((e*(a + b*x))/(c + d*x))))/(30*b^3*d^3) + (B^2*(b*c - a*d)^5*g^2*i^2*log(c + d*x))/(10*b^3*d^3) + (B^2*(b*c - a*d)^5*g^2*i^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(15*b^3*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 14, (B^2*(b*c - a*d)^3*g*i^2*x)/(12*b^2*d) + (B^2*(b*c - a*d)^2*g*i^2*(c + d*x)^2)/(12*b*d^2) - (B^2*(b*c - a*d)^4*g*i^2*log((a + b*x)/(c + d*x)))/(12*b^3*d^2) - (B*(b*c - a*d)^3*g*i^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(6*b^3*d) - (B*(b*c - a*d)^2*g*i^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(6*b^3) + (B*(b*c - a*d)^2*g*i^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*b*d^2) - (B*(b*c - a*d)*g*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(6*d^2) + ((b*c - a*d)^2*g*i^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(12*b^3) + ((b*c - a*d)*g*i^2*(a + b*x)^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(6*b^2) + (g*i^2*(a + b*x)^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(4*b) - (B*(b*c - a*d)^4*g*i^2*log((b*c - a*d)/(b*(c + d*x)))*(A + B + B*log((e*(a + b*x))/(c + d*x))))/(6*b^3*d^2) - (B^2*(b*c - a*d)^4*g*i^2*log(c + d*x))/(4*b^3*d^2) - (B^2*(b*c - a*d)^4*g*i^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(6*b^3*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 11, (B^2*(b*c - a*d)^2*i^2*x)/(3*b^2) + (B^2*(b*c - a*d)^3*i^2*log((a + b*x)/(c + d*x)))/(3*b^3*d) - (2*B*(b*c - a*d)^2*i^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*b^3) - (B*(b*c - a*d)*i^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*b*d) + (i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*d) + (B^2*(b*c - a*d)^3*i^2*log(c + d*x))/(b^3*d) + (2*B*(b*c - a*d)^3*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(3*b^3*d) - (2*B^2*(b*c - a*d)^3*i^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(3*b^3*d)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^1, x, 15, -((B*d*(b*c - a*d)*i^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g)) + (2*B*(b*c - a*d)^2*i^2*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g) + (d*(b*c - a*d)*i^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^3*g) + (i^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*b*g) + (B^2*(b*c - a*d)^2*i^2*log(c + d*x))/(b^3*g) + (B*(b*c - a*d)^2*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) - ((b*c - a*d)^2*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) + (2*B^2*(b*c - a*d)^2*i^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^3*g) - (B^2*(b*c - a*d)^2*i^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) + (2*B*(b*c - a*d)^2*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) + (2*B^2*(b*c - a*d)^2*i^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^2, x, 11, -((2*B^2*(b*c - a*d)*i^2*(c + d*x))/(b^2*g^2*(a + b*x))) - (2*B*(b*c - a*d)*i^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^2*g^2*(a + b*x)) + (2*B*d*(b*c - a*d)*i^2*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g^2) + (d^2*i^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^3*g^2) - ((b*c - a*d)*i^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^2*g^2*(a + b*x)) - (2*d*(b*c - a*d)*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2) + (2*B^2*d*(b*c - a*d)*i^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^3*g^2) + (4*B*d*(b*c - a*d)*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2) + (4*B^2*d*(b*c - a*d)*i^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^3, x, 10, -((2*B^2*d*i^2*(c + d*x))/(b^2*g^3*(a + b*x))) - (B^2*i^2*(c + d*x)^2)/(4*b*g^3*(a + b*x)^2) - (2*B*d*i^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^2*g^3*(a + b*x)) - (B*i^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*b*g^3*(a + b*x)^2) - (d*i^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^2*g^3*(a + b*x)) - (i^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*b*g^3*(a + b*x)^2) - (d^2*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3) + (2*B*d^2*i^2*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3) + (2*B^2*d^2*i^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^4, x, 3, -((2*B^2*i^2*(c + d*x)^3)/(27*(b*c - a*d)*g^4*(a + b*x)^3)) - (2*B*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(9*(b*c - a*d)*g^4*(a + b*x)^3) - (i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*(b*c - a*d)*g^4*(a + b*x)^3)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^5, x, 7, (2*B^2*d*i^2*(c + d*x)^3)/(27*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*B^2*i^2*(c + d*x)^4)/(32*(b*c - a*d)^2*g^5*(a + b*x)^4) + (2*B*d*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(9*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*B*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(8*(b*c - a*d)^2*g^5*(a + b*x)^4) + (d*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(4*(b*c - a*d)^2*g^5*(a + b*x)^4)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^6, x, 9, -((2*B^2*d^2*i^2*(c + d*x)^3)/(27*(b*c - a*d)^3*g^6*(a + b*x)^3)) + (b*B^2*d*i^2*(c + d*x)^4)/(16*(b*c - a*d)^3*g^6*(a + b*x)^4) - (2*b^2*B^2*i^2*(c + d*x)^5)/(125*(b*c - a*d)^3*g^6*(a + b*x)^5) - (2*B*d^2*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(9*(b*c - a*d)^3*g^6*(a + b*x)^3) + (b*B*d*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*(b*c - a*d)^3*g^6*(a + b*x)^4) - (2*b^2*B*i^2*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(25*(b*c - a*d)^3*g^6*(a + b*x)^5) - (d^2*i^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*(b*c - a*d)^3*g^6*(a + b*x)^3) + (b*d*i^2*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^3*g^6*(a + b*x)^4) - (b^2*i^2*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(5*(b*c - a*d)^3*g^6*(a + b*x)^5)]


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 22, (5*B^2*(b*c - a*d)^6*g^3*i^3*x)/(84*b^3*d^3) + (B^2*(b*c - a*d)^3*g^3*i^3*(a + b*x)^4)/(140*b^4) - (29*B^2*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2)/(840*b^2*d^4) + (47*B^2*(b*c - a*d)^4*g^3*i^3*(c + d*x)^3)/(1260*b*d^4) - (13*B^2*(b*c - a*d)^3*g^3*i^3*(c + d*x)^4)/(420*d^4) + (b*B^2*(b*c - a*d)^2*g^3*i^3*(c + d*x)^5)/(105*d^4) - (B^2*(b*c - a*d)^7*g^3*i^3*log((a + b*x)/(c + d*x)))/(210*b^4*d^4) - (B*(b*c - a*d)^4*g^3*i^3*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(210*b^4*d) - (3*B*(b*c - a*d)^3*g^3*i^3*(a + b*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(140*b^4) - (B*(b*c - a*d)^2*g^3*i^3*(a + b*x)^4*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(35*b^3) + (2*B*(b*c - a*d)^4*g^3*i^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(21*b*d^4) - (3*B*(b*c - a*d)^3*g^3*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(14*d^4) + (6*b*B*(b*c - a*d)^2*g^3*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(35*d^4) - (b^2*B*(b*c - a*d)*g^3*i^3*(c + d*x)^6*(A + B*log((e*(a + b*x))/(c + d*x))))/(21*d^4) + ((b*c - a*d)^3*g^3*i^3*(a + b*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(140*b^4) + ((b*c - a*d)^2*g^3*i^3*(a + b*x)^4*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(35*b^3) + ((b*c - a*d)*g^3*i^3*(a + b*x)^4*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(14*b^2) + (g^3*i^3*(a + b*x)^4*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(7*b) + (B*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2*(3*A + B + 3*B*log((e*(a + b*x))/(c + d*x))))/(420*b^4*d^2) - (B*(b*c - a*d)^6*g^3*i^3*(a + b*x)*(6*A + 5*B + 6*B*log((e*(a + b*x))/(c + d*x))))/(420*b^4*d^3) - (B*(b*c - a*d)^7*g^3*i^3*log((b*c - a*d)/(b*(c + d*x)))*(6*A + 11*B + 6*B*log((e*(a + b*x))/(c + d*x))))/(420*b^4*d^4) - (11*B^2*(b*c - a*d)^7*g^3*i^3*log(c + d*x))/(420*b^4*d^4) - (B^2*(b*c - a*d)^7*g^3*i^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(70*b^4*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 20, -((7*B^2*(b*c - a*d)^5*g^2*i^3*x)/(180*b^3*d^2)) - (7*B^2*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2)/(360*b^2*d^3) - (B^2*(b*c - a*d)^3*g^2*i^3*(c + d*x)^3)/(60*b*d^3) + (B^2*(b*c - a*d)^2*g^2*i^3*(c + d*x)^4)/(60*d^3) + (B^2*(b*c - a*d)^6*g^2*i^3*log((a + b*x)/(c + d*x)))/(36*b^4*d^3) - (B*(b*c - a*d)^4*g^2*i^3*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(60*b^4*d) - (B*(b*c - a*d)^3*g^2*i^3*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(30*b^4) - (B*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(10*b^2*d^3) + (B*(b*c - a*d)^3*g^2*i^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(45*b*d^3) + (7*B*(b*c - a*d)^2*g^2*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(60*d^3) - (b*B*(b*c - a*d)*g^2*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(15*d^3) + ((b*c - a*d)^3*g^2*i^3*(a + b*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(60*b^4) + ((b*c - a*d)^2*g^2*i^3*(a + b*x)^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(20*b^3) + ((b*c - a*d)*g^2*i^3*(a + b*x)^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(10*b^2) + (g^2*i^3*(a + b*x)^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(6*b) + (B*(b*c - a*d)^5*g^2*i^3*(a + b*x)*(2*A + B + 2*B*log((e*(a + b*x))/(c + d*x))))/(60*b^4*d^2) + (B*(b*c - a*d)^6*g^2*i^3*log((b*c - a*d)/(b*(c + d*x)))*(2*A + 3*B + 2*B*log((e*(a + b*x))/(c + d*x))))/(60*b^4*d^3) + (11*B^2*(b*c - a*d)^6*g^2*i^3*log(c + d*x))/(180*b^4*d^3) + (B^2*(b*c - a*d)^6*g^2*i^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(30*b^4*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 19, (B^2*(b*c - a*d)^4*g*i^3*x)/(60*b^3*d) + (B^2*(b*c - a*d)^3*g*i^3*(c + d*x)^2)/(30*b^2*d^2) + (B^2*(b*c - a*d)^2*g*i^3*(c + d*x)^3)/(30*b*d^2) - (B^2*(b*c - a*d)^5*g*i^3*log((a + b*x)/(c + d*x)))/(12*b^4*d^2) - (B*(b*c - a*d)^4*g*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(10*b^4*d) - (B*(b*c - a*d)^3*g*i^3*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(10*b^4) + (3*B*(b*c - a*d)^3*g*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(20*b^2*d^2) + (B*(b*c - a*d)^2*g*i^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(30*b*d^2) - (B*(b*c - a*d)*g*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(10*d^2) + ((b*c - a*d)^3*g*i^3*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(20*b^4) + ((b*c - a*d)^2*g*i^3*(a + b*x)^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(10*b^3) + (3*(b*c - a*d)*g*i^3*(a + b*x)^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(20*b^2) + (g*i^3*(a + b*x)^2*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(5*b) - (B*(b*c - a*d)^5*g*i^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B + B*log((e*(a + b*x))/(c + d*x))))/(10*b^4*d^2) - (11*B^2*(b*c - a*d)^5*g*i^3*log(c + d*x))/(60*b^4*d^2) - (B^2*(b*c - a*d)^5*g*i^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(10*b^4*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2, x, 15, (5*B^2*(b*c - a*d)^3*i^3*x)/(12*b^3) + (B^2*(b*c - a*d)^2*i^3*(c + d*x)^2)/(12*b^2*d) + (5*B^2*(b*c - a*d)^4*i^3*log((a + b*x)/(c + d*x)))/(12*b^4*d) - (B*(b*c - a*d)^3*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*b^4) - (B*(b*c - a*d)^2*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(4*b^2*d) - (B*(b*c - a*d)*i^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(6*b*d) + (i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(4*d) + (11*B^2*(b*c - a*d)^4*i^3*log(c + d*x))/(12*b^4*d) + (B*(b*c - a*d)^4*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(2*b^4*d) - (B^2*(b*c - a*d)^4*i^3*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(2*b^4*d)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^1, x, 26, (B^2*d*(b*c - a*d)^2*i^3*x)/(3*b^3*g) + (B^2*(b*c - a*d)^3*i^3*log((a + b*x)/(c + d*x)))/(3*b^4*g) - (5*B*d*(b*c - a*d)^2*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*b^4*g) - (B*(b*c - a*d)*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*b^2*g) + (2*B*(b*c - a*d)^3*i^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^4*g) + (d*(b*c - a*d)^2*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^4*g) + ((b*c - a*d)*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*b^2*g) + (i^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*b*g) + (2*B^2*(b*c - a*d)^3*i^3*log(c + d*x))/(b^4*g) + (5*B*(b*c - a*d)^3*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(3*b^4*g) - ((b*c - a*d)^3*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g) + (2*B^2*(b*c - a*d)^3*i^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^4*g) - (5*B^2*(b*c - a*d)^3*i^3*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(3*b^4*g) + (2*B*(b*c - a*d)^3*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g) + (2*B^2*(b*c - a*d)^3*i^3*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^2, x, 17, -((2*B^2*(b*c - a*d)^2*i^3*(c + d*x))/(b^3*g^2*(a + b*x))) - (B*d^2*(b*c - a*d)*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^4*g^2) - (2*B*(b*c - a*d)^2*i^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g^2*(a + b*x)) + (4*B*d*(b*c - a*d)^2*i^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^4*g^2) + (2*d^2*(b*c - a*d)*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^4*g^2) - ((b*c - a*d)^2*i^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^3*g^2*(a + b*x)) + (d*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*b^2*g^2) + (B^2*d*(b*c - a*d)^2*i^3*log(c + d*x))/(b^4*g^2) + (B*d*(b*c - a*d)^2*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) - (3*d*(b*c - a*d)^2*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) + (4*B^2*d*(b*c - a*d)^2*i^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^4*g^2) - (B^2*d*(b*c - a*d)^2*i^3*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) + (6*B*d*(b*c - a*d)^2*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) + (6*B^2*d*(b*c - a*d)^2*i^3*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^3, x, 13, -((4*B^2*d*(b*c - a*d)*i^3*(c + d*x))/(b^3*g^3*(a + b*x))) - (B^2*(b*c - a*d)*i^3*(c + d*x)^2)/(4*b^2*g^3*(a + b*x)^2) - (4*B*d*(b*c - a*d)*i^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^3*g^3*(a + b*x)) - (B*(b*c - a*d)*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*b^2*g^3*(a + b*x)^2) + (2*B*d^2*(b*c - a*d)*i^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(b^4*g^3) + (d^3*i^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^4*g^3) - (2*d*(b*c - a*d)*i^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(b^3*g^3*(a + b*x)) - ((b*c - a*d)*i^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*b^2*g^3*(a + b*x)^2) - (3*d^2*(b*c - a*d)*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3) + (2*B^2*d^2*(b*c - a*d)*i^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^4*g^3) + (6*B*d^2*(b*c - a*d)*i^3*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3) + (6*B^2*d^2*(b*c - a*d)*i^3*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^5, x, 3, -((B^2*i^3*(c + d*x)^4)/(32*(b*c - a*d)*g^5*(a + b*x)^4)) - (B*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(8*(b*c - a*d)*g^5*(a + b*x)^4) - (i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(4*(b*c - a*d)*g^5*(a + b*x)^4)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^6, x, 7, (B^2*d*i^3*(c + d*x)^4)/(32*(b*c - a*d)^2*g^6*(a + b*x)^4) - (2*b*B^2*i^3*(c + d*x)^5)/(125*(b*c - a*d)^2*g^6*(a + b*x)^5) + (B*d*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(8*(b*c - a*d)^2*g^6*(a + b*x)^4) - (2*b*B*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(25*(b*c - a*d)^2*g^6*(a + b*x)^5) + (d*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(4*(b*c - a*d)^2*g^6*(a + b*x)^4) - (b*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(5*(b*c - a*d)^2*g^6*(a + b*x)^5)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(a*g + b*g*x)^7, x, 9, -((B^2*d^2*i^3*(c + d*x)^4)/(32*(b*c - a*d)^3*g^7*(a + b*x)^4)) + (4*b*B^2*d*i^3*(c + d*x)^5)/(125*(b*c - a*d)^3*g^7*(a + b*x)^5) - (b^2*B^2*i^3*(c + d*x)^6)/(108*(b*c - a*d)^3*g^7*(a + b*x)^6) - (B*d^2*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x))))/(8*(b*c - a*d)^3*g^7*(a + b*x)^4) + (4*b*B*d*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x))))/(25*(b*c - a*d)^3*g^7*(a + b*x)^5) - (b^2*B*i^3*(c + d*x)^6*(A + B*log((e*(a + b*x))/(c + d*x))))/(18*(b*c - a*d)^3*g^7*(a + b*x)^6) - (d^2*i^3*(c + d*x)^4*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(4*(b*c - a*d)^3*g^7*(a + b*x)^4) + (2*b*d*i^3*(c + d*x)^5*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(5*(b*c - a*d)^3*g^7*(a + b*x)^5) - (b^2*i^3*(c + d*x)^6*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(6*(b*c - a*d)^3*g^7*(a + b*x)^6)]


    #= ::Subsubsection::Closed:: =#
    #=q<0=#


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x), x, 25, (b*B^2*(b*c - a*d)^2*g^3*x)/(3*d^3*i) + (B^2*(b*c - a*d)^3*g^3*log((a + b*x)/(c + d*x)))/(3*d^4*i) + (7*B*(b*c - a*d)^2*g^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*d^3*i) - (b^2*B*(b*c - a*d)*g^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(3*d^4*i) + (6*B*(b*c - a*d)^3*g^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^4*i) + (3*(b*c - a*d)^2*g^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^3*i) - (3*b^2*(b*c - a*d)*g^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*d^4*i) + (b^3*g^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*d^4*i) + ((b*c - a*d)^3*g^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^4*i) - (2*B^2*(b*c - a*d)^3*g^3*log(c + d*x))/(d^4*i) - (7*B*(b*c - a*d)^3*g^3*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(3*d^4*i) + (6*B^2*(b*c - a*d)^3*g^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i) + (2*B*(b*c - a*d)^3*g^3*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i) + (7*B^2*(b*c - a*d)^3*g^3*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(3*d^4*i) - (2*B^2*(b*c - a*d)^3*g^3*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x), x, 15, -((B*(b*c - a*d)*g^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^2*i)) - (4*B*(b*c - a*d)^2*g^2*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^3*i) - (2*(b*c - a*d)*g^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^2*i) + (b^2*g^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*d^3*i) - ((b*c - a*d)^2*g^2*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^3*i) + (B^2*(b*c - a*d)^2*g^2*log(c + d*x))/(d^3*i) + (B*(b*c - a*d)^2*g^2*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(d^3*i) - (4*B^2*(b*c - a*d)^2*g^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i) - (2*B*(b*c - a*d)^2*g^2*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i) - (B^2*(b*c - a*d)^2*g^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(d^3*i) + (2*B^2*(b*c - a*d)^2*g^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x), x, 9, (2*B*(b*c - a*d)*g*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^2*i) + (g*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d*i) + ((b*c - a*d)*g*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^2*i) + (2*B^2*(b*c - a*d)*g*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i) + (2*B*(b*c - a*d)*g*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i) - (2*B^2*(b*c - a*d)*g*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x), x, 4, -((log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d*i)) - (2*B*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d*i) + (2*B^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d*i)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^1*(c*i + d*i*x)), x, 3, (A + B*log((e*(a + b*x))/(c + d*x)))^3/(3*B*(b*c - a*d)*g*i)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^2*(c*i + d*i*x)), x, 7, -((2*b*B^2*(c + d*x))/((b*c - a*d)^2*g^2*i*(a + b*x))) - (2*b*B*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^2*g^2*i*(a + b*x)) - (b*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^2*g^2*i*(a + b*x)) - (d*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(3*B*(b*c - a*d)^2*g^2*i)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^3*(c*i + d*i*x)), x, 9, (4*b*B^2*d*(c + d*x))/((b*c - a*d)^3*g^3*i*(a + b*x)) - (b^2*B^2*(c + d*x)^2)/(4*(b*c - a*d)^3*g^3*i*(a + b*x)^2) + (4*b*B*d*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^3*g^3*i*(a + b*x)) - (b^2*B*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^3*g^3*i*(a + b*x)^2) + (2*b*d*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^3*g^3*i*(a + b*x)) - (b^2*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^3*g^3*i*(a + b*x)^2) + (d^2*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(3*B*(b*c - a*d)^3*g^3*i)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^4*(c*i + d*i*x)), x, 11, -((6*b*B^2*d^2*(c + d*x))/((b*c - a*d)^4*g^4*i*(a + b*x))) + (3*b^2*B^2*d*(c + d*x)^2)/(4*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (2*b^3*B^2*(c + d*x)^3)/(27*(b*c - a*d)^4*g^4*i*(a + b*x)^3) - (6*b*B*d^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^4*i*(a + b*x)) + (3*b^2*B*d*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (2*b^3*B*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(9*(b*c - a*d)^4*g^4*i*(a + b*x)^3) - (3*b*d^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^4*g^4*i*(a + b*x)) + (3*b^2*d*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (b^3*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*(b*c - a*d)^4*g^4*i*(a + b*x)^3) - (d^3*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(3*B*(b*c - a*d)^4*g^4*i)]


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x)^2, x, 18, (2*A*B*(b*c - a*d)^2*g^3*(a + b*x))/(d^3*i^2*(c + d*x)) - (2*B^2*(b*c - a*d)^2*g^3*(a + b*x))/(d^3*i^2*(c + d*x)) + (2*B^2*(b*c - a*d)^2*g^3*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d^3*i^2*(c + d*x)) - (b*B*(b*c - a*d)*g^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^3*i^2) - (6*b*B*(b*c - a*d)^2*g^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^4*i^2) - (3*b*(b*c - a*d)*g^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^3*i^2) - ((b*c - a*d)^2*g^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^3*i^2*(c + d*x)) + (b^3*g^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*d^4*i^2) - (3*b*(b*c - a*d)^2*g^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^4*i^2) + (b*B^2*(b*c - a*d)^2*g^3*log(c + d*x))/(d^4*i^2) + (b*B*(b*c - a*d)^2*g^3*(A + B*log((e*(a + b*x))/(c + d*x)))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(d^4*i^2) - (6*b*B^2*(b*c - a*d)^2*g^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^2) - (6*b*B*(b*c - a*d)^2*g^3*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^2) - (b*B^2*(b*c - a*d)^2*g^3*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(d^4*i^2) + (6*b*B^2*(b*c - a*d)^2*g^3*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^2)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x)^2, x, 12, -((2*A*B*(b*c - a*d)*g^2*(a + b*x))/(d^2*i^2*(c + d*x))) + (2*B^2*(b*c - a*d)*g^2*(a + b*x))/(d^2*i^2*(c + d*x)) - (2*B^2*(b*c - a*d)*g^2*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d^2*i^2*(c + d*x)) + (2*b*B*(b*c - a*d)*g^2*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^3*i^2) + (b*g^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^2*i^2) + ((b*c - a*d)*g^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^2*i^2*(c + d*x)) + (2*b*(b*c - a*d)*g^2*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^3*i^2) + (2*b*B^2*(b*c - a*d)*g^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^2) + (4*b*B*(b*c - a*d)*g^2*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^2) - (4*b*B^2*(b*c - a*d)*g^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^2)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x)^2, x, 9, (2*A*B*g*(a + b*x))/(d*i^2*(c + d*x)) - (2*B^2*g*(a + b*x))/(d*i^2*(c + d*x)) + (2*B^2*g*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d*i^2*(c + d*x)) - (g*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d*i^2*(c + d*x)) - (b*g*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^2*i^2) - (2*b*B*g*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i^2) + (2*b*B^2*g*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i^2)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x)^2, x, 4, -((2*A*B*(a + b*x))/((b*c - a*d)*i^2*(c + d*x))) + (2*B^2*(a + b*x))/((b*c - a*d)*i^2*(c + d*x)) - (2*B^2*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)*i^2*(c + d*x)) + ((a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)*i^2*(c + d*x))]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^1*(c*i + d*i*x)^2), x, 7, (2*A*B*d*(a + b*x))/((b*c - a*d)^2*g*i^2*(c + d*x)) - (2*B^2*d*(a + b*x))/((b*c - a*d)^2*g*i^2*(c + d*x)) + (2*B^2*d*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^2*g*i^2*(c + d*x)) - (d*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^2*g*i^2*(c + d*x)) + (b*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(3*B*(b*c - a*d)^2*g*i^2)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^2*(c*i + d*i*x)^2), x, 10, -((2*A*B*d^2*(a + b*x))/((b*c - a*d)^3*g^2*i^2*(c + d*x))) + (2*B^2*d^2*(a + b*x))/((b*c - a*d)^3*g^2*i^2*(c + d*x)) - (2*b^2*B^2*(c + d*x))/((b*c - a*d)^3*g^2*i^2*(a + b*x)) - (2*B^2*d^2*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^3*g^2*i^2*(c + d*x)) - (2*b^2*B*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^3*g^2*i^2*(a + b*x)) + (d^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^3*g^2*i^2*(c + d*x)) - (b^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^3*g^2*i^2*(a + b*x)) - (2*b*d*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(3*B*(b*c - a*d)^3*g^2*i^2)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^3*(c*i + d*i*x)^2), x, 12, (2*A*B*d^3*(a + b*x))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) - (2*B^2*d^3*(a + b*x))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (6*b^2*B^2*d*(c + d*x))/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*B^2*(c + d*x)^2)/(4*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) + (2*B^2*d^3*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (6*b^2*B*d*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*B*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) - (d^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (3*b^2*d*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) + (b*d^2*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(B*(b*c - a*d)^4*g^3*i^2)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^4*(c*i + d*i*x)^2), x, 14, -((2*A*B*d^4*(a + b*x))/((b*c - a*d)^5*g^4*i^2*(c + d*x))) + (2*B^2*d^4*(a + b*x))/((b*c - a*d)^5*g^4*i^2*(c + d*x)) - (12*b^2*B^2*d^2*(c + d*x))/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (b^3*B^2*d*(c + d*x)^2)/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (2*b^4*B^2*(c + d*x)^3)/(27*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) - (2*B^2*d^4*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^5*g^4*i^2*(c + d*x)) - (12*b^2*B*d^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (2*b^3*B*d*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (2*b^4*B*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(9*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) + (d^4*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^5*g^4*i^2*(c + d*x)) - (6*b^2*d^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (2*b^3*d*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (b^4*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) - (4*b*d^3*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(3*B*(b*c - a*d)^5*g^4*i^2)]


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x)^3, x, 14, (B^2*(b*c - a*d)*g^3*(a + b*x)^2)/(4*d^2*i^3*(c + d*x)^2) - (4*A*b*B*(b*c - a*d)*g^3*(a + b*x))/(d^3*i^3*(c + d*x)) + (4*b*B^2*(b*c - a*d)*g^3*(a + b*x))/(d^3*i^3*(c + d*x)) - (4*b*B^2*(b*c - a*d)*g^3*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d^3*i^3*(c + d*x)) - (B*(b*c - a*d)*g^3*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*d^2*i^3*(c + d*x)^2) + (2*b^2*B*(b*c - a*d)*g^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x))))/(d^4*i^3) + (b^2*g^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^3*i^3) + ((b*c - a*d)*g^3*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*d^2*i^3*(c + d*x)^2) + (2*b*(b*c - a*d)*g^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^3*i^3*(c + d*x)) + (3*b^2*(b*c - a*d)*g^3*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^4*i^3) + (2*b^2*B^2*(b*c - a*d)*g^3*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^3) + (6*b^2*B*(b*c - a*d)*g^3*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^3) - (6*b^2*B^2*(b*c - a*d)*g^3*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^3)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x)^3, x, 11, -((B^2*g^2*(a + b*x)^2)/(4*d*i^3*(c + d*x)^2)) + (2*A*b*B*g^2*(a + b*x))/(d^2*i^3*(c + d*x)) - (2*b*B^2*g^2*(a + b*x))/(d^2*i^3*(c + d*x)) + (2*b*B^2*g^2*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/(d^2*i^3*(c + d*x)) + (B*g^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*d*i^3*(c + d*x)^2) - (g^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*d*i^3*(c + d*x)^2) - (b*g^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^2*i^3*(c + d*x)) - (b^2*g^2*log((b*c - a*d)/(b*(c + d*x)))*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(d^3*i^3) - (2*b^2*B*g^2*(A + B*log((e*(a + b*x))/(c + d*x)))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^3) + (2*b^2*B^2*g^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^3)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x)^3, x, 3, (B^2*g*(a + b*x)^2)/(4*(b*c - a*d)*i^3*(c + d*x)^2) - (B*g*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)*i^3*(c + d*x)^2) + (g*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)*i^3*(c + d*x)^2)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*(a + b*x)/(c + d*x)))^2/(c*i + d*i*x)^3, x, 8, -((B^2*d*(a + b*x)^2)/(4*(b*c - a*d)^2*i^3*(c + d*x)^2)) - (2*A*b*B*(a + b*x))/((b*c - a*d)^2*i^3*(c + d*x)) + (2*b*B^2*(a + b*x))/((b*c - a*d)^2*i^3*(c + d*x)) - (2*b*B^2*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^2*i^3*(c + d*x)) + (B*d*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^2*i^3*(c + d*x)^2) - (d*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^2*i^3*(c + d*x)^2) + (b*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^2*i^3*(c + d*x))]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^1*(c*i + d*i*x)^3), x, 15, (B^2*d^2*(a + b*x)^2)/(4*(b*c - a*d)^3*g*i^3*(c + d*x)^2) + (4*A*b*B*d*(a + b*x))/((b*c - a*d)^3*g*i^3*(c + d*x)) - (4*b*B^2*d*(a + b*x))/((b*c - a*d)^3*g*i^3*(c + d*x)) + (4*b*B^2*d*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^3*g*i^3*(c + d*x)) - (B*d^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^3*g*i^3*(c + d*x)^2) + (d^2*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^3*g*i^3*(c + d*x)^2) - (2*b*d*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^3*g*i^3*(c + d*x)) + (b^2*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(3*B*(b*c - a*d)^3*g*i^3)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^2*(c*i + d*i*x)^3), x, 12, -((B^2*d^3*(a + b*x)^2)/(4*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2)) - (6*A*b*B*d^2*(a + b*x))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) + (6*b*B^2*d^2*(a + b*x))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) - (2*b^3*B^2*(c + d*x))/((b*c - a*d)^4*g^2*i^3*(a + b*x)) - (6*b*B^2*d^2*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) + (B*d^3*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2) - (2*b^3*B*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^4*g^2*i^3*(a + b*x)) - (d^3*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2) + (3*b*d^2*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^4*g^2*i^3*(c + d*x)) - (b^3*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^4*g^2*i^3*(a + b*x)) - (b^2*d*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(B*(b*c - a*d)^4*g^2*i^3)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^3*(c*i + d*i*x)^3), x, 14, (B^2*d^4*(a + b*x)^2)/(4*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2) + (8*A*b*B*d^3*(a + b*x))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) - (8*b*B^2*d^3*(a + b*x))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) + (8*b^3*B^2*d*(c + d*x))/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*B^2*(c + d*x)^2)/(4*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) + (8*b*B^2*d^3*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) - (B*d^4*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2) + (8*b^3*B*d*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*B*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) + (d^4*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2) - (4*b*d^3*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^5*g^3*i^3*(c + d*x)) + (4*b^3*d*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) + (2*b^2*d^2*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(B*(b*c - a*d)^5*g^3*i^3)]
    @test_int [(A + B*log(e*(a + b*x)/(c + d*x)))^2/((a*g + b*g*x)^4*(c*i + d*i*x)^3), x, 16, -((B^2*d^5*(a + b*x)^2)/(4*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2)) - (10*A*b*B*d^4*(a + b*x))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) + (10*b*B^2*d^4*(a + b*x))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) - (20*b^3*B^2*d^2*(c + d*x))/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*B^2*d*(c + d*x)^2)/(4*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (2*b^5*B^2*(c + d*x)^3)/(27*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) - (10*b*B^2*d^4*(a + b*x)*log((e*(a + b*x))/(c + d*x)))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) + (B*d^5*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2) - (20*b^3*B*d^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x))))/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*B*d*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x))))/(2*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (2*b^5*B*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x))))/(9*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) - (d^5*(a + b*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2) + (5*b*d^4*(a + b*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^6*g^4*i^3*(c + d*x)) - (10*b^3*d^2*(c + d*x)*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*d*(c + d*x)^2*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(2*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (b^5*(c + d*x)^3*(A + B*log((e*(a + b*x))/(c + d*x)))^2)/(3*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) - (10*b^2*d^3*(A + B*log((e*(a + b*x))/(c + d*x)))^3)/(3*B*(b*c - a*d)^6*g^4*i^3)]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*((a+b*x) / (c+d*x))^n))^1*when*b*f-a*g=0*and*d*h-c*i=0=#


    #= ::Subsubsection::Closed:: =#
    #=q>0=#


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 5, -((B*(b*c - a*d)^4*g^3*i*n*x)/(20*b*d^3)) + (B*(b*c - a*d)^3*g^3*i*n*(a + b*x)^2)/(40*b^2*d^2) - (B*(b*c - a*d)^2*g^3*i*n*(a + b*x)^3)/(60*b^2*d) + (g^3*i*(a + b*x)^4*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(5*b) + ((b*c - a*d)*g^3*i*(a + b*x)^4*(A - B*n + B*log(e*((a + b*x)/(c + d*x))^n)))/(20*b^2) + (B*(b*c - a*d)^5*g^3*i*n*log(c + d*x))/(20*b^2*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 5, (B*(b*c - a*d)^3*g^2*i*n*x)/(12*b*d^2) - (B*(b*c - a*d)^2*g^2*i*n*(a + b*x)^2)/(24*b^2*d) + (g^2*i*(a + b*x)^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*b) + ((b*c - a*d)*g^2*i*(a + b*x)^3*(A - B*n + B*log(e*((a + b*x)/(c + d*x))^n)))/(12*b^2) - (B*(b*c - a*d)^4*g^2*i*n*log(c + d*x))/(12*b^2*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 5, -((B*(b*c - a*d)^2*g*i*n*x)/(6*b*d)) + (g*i*(a + b*x)^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*b) + ((b*c - a*d)*g*i*(a + b*x)^2*(A - B*n + B*log(e*((a + b*x)/(c + d*x))^n)))/(6*b^2) + (B*(b*c - a*d)^3*g*i*n*log(c + d*x))/(6*b^2*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 4, -(B*(b*c - a*d)*i*n*x)/(2*b) - (B*(b*c - a*d)^2*i*n*log(a + b*x))/(2*b^2*d) + (i*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^1, x, 6, (i*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b*g) - ((b*c - a*d)*i*log(-((b*c - a*d)/(d*(a + b*x))))*(A - B*n + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^2*g) + (B*(b*c - a*d)*i*n*PolyLog(2, 1 + (b*c - a*d)/(d*(a + b*x))))/(b^2*g)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^2, x, 5, -((B*i*n*(c + d*x))/(b*g^2*(a + b*x))) - (i*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b*g^2*(a + b*x)) - (d*i*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2) + (B*d*i*n*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^3, x, 2, -(B*i*n*(c + d*x)^2)/(4*(b*c - a*d)*g^3*(a + b*x)^2) - (i*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)*g^3*(a + b*x)^2)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^4, x, 5, (B*d*i*n*(c + d*x)^2)/(4*(b*c - a*d)^2*g^4*(a + b*x)^2) - (b*B*i*n*(c + d*x)^3)/(9*(b*c - a*d)^2*g^4*(a + b*x)^3) + (d*i*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^2*g^4*(a + b*x)^2) - (b*i*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*(b*c - a*d)^2*g^4*(a + b*x)^3)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^5, x, 5, -(B*d^2*i*n*(c + d*x)^2)/(4*(b*c - a*d)^3*g^5*(a + b*x)^2) + (2*b*B*d*i*n*(c + d*x)^3)/(9*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*B*i*n*(c + d*x)^4)/(16*(b*c - a*d)^3*g^5*(a + b*x)^4) - (d^2*i*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^3*g^5*(a + b*x)^2) + (2*b*d*i*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*i*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*(b*c - a*d)^3*g^5*(a + b*x)^4)]


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 5, (B*(b*c - a*d)^5*g^3*i^2*n*x)/(60*b^2*d^3) + (B*(b*c - a*d)^4*g^3*i^2*n*(c + d*x)^2)/(120*b*d^4) - (19*B*(b*c - a*d)^3*g^3*i^2*n*(c + d*x)^3)/(180*d^4) + (13*b*B*(b*c - a*d)^2*g^3*i^2*n*(c + d*x)^4)/(120*d^4) - (b^2*B*(b*c - a*d)*g^3*i^2*n*(c + d*x)^5)/(30*d^4) - ((b*c - a*d)^3*g^3*i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*d^4) + (3*b*(b*c - a*d)^2*g^3*i^2*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*d^4) - (3*b^2*(b*c - a*d)*g^3*i^2*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(5*d^4) + (b^3*g^3*i^2*(c + d*x)^6*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(6*d^4) + (B*(b*c - a*d)^6*g^3*i^2*n*log((a + b*x)/(c + d*x)))/(60*b^3*d^4) + (B*(b*c - a*d)^6*g^3*i^2*n*log(c + d*x))/(60*b^3*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 5, -((B*(b*c - a*d)^4*g^2*i^2*n*x)/(30*b^2*d^2)) - (B*(b*c - a*d)^3*g^2*i^2*n*(c + d*x)^2)/(60*b*d^3) + (B*(b*c - a*d)^2*g^2*i^2*n*(c + d*x)^3)/(10*d^3) - (b*B*(b*c - a*d)*g^2*i^2*n*(c + d*x)^4)/(20*d^3) + ((b*c - a*d)^2*g^2*i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*d^3) - (b*(b*c - a*d)*g^2*i^2*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d^3) + (b^2*g^2*i^2*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(5*d^3) - (B*(b*c - a*d)^5*g^2*i^2*n*log((a + b*x)/(c + d*x)))/(30*b^3*d^3) - (B*(b*c - a*d)^5*g^2*i^2*n*log(c + d*x))/(30*b^3*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 5, (B*(b*c - a*d)^3*g*i^2*n*x)/(12*b^2*d) + (B*(b*c - a*d)^2*g*i^2*n*(c + d*x)^2)/(24*b*d^2) - (B*(b*c - a*d)*g*i^2*n*(c + d*x)^3)/(12*d^2) - ((b*c - a*d)*g*i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*d^2) + (b*g*i^2*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*d^2) + (B*(b*c - a*d)^4*g*i^2*n*log((a + b*x)/(c + d*x)))/(12*b^3*d^2) + (B*(b*c - a*d)^4*g*i^2*n*log(c + d*x))/(12*b^3*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 4, -(B*(b*c - a*d)^2*i^2*n*x)/(3*b^2) - (B*(b*c - a*d)*i^2*n*(c + d*x)^2)/(6*b*d) - (B*(b*c - a*d)^3*i^2*n*log(a + b*x))/(3*b^3*d) + (i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*d)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^1, x, 10, -((B*d*(b*c - a*d)*i^2*n*x)/(2*b^2*g)) + (d*(b*c - a*d)*i^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^3*g) + (i^2*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b*g) - (B*(b*c - a*d)^2*i^2*n*log((a + b*x)/(c + d*x)))/(2*b^3*g) - (3*B*(b*c - a*d)^2*i^2*n*log(c + d*x))/(2*b^3*g) - ((b*c - a*d)^2*i^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) + (B*(b*c - a*d)^2*i^2*n*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^2, x, 8, -((B*(b*c - a*d)*i^2*n*(c + d*x))/(b^2*g^2*(a + b*x))) + (d^2*i^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^3*g^2) - ((b*c - a*d)*i^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^2*g^2*(a + b*x)) - (B*d*(b*c - a*d)*i^2*n*log(c + d*x))/(b^3*g^2) - (2*d*(b*c - a*d)*i^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2) + (2*B*d*(b*c - a*d)*i^2*n*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^3, x, 7, -((B*d*i^2*n*(c + d*x))/(b^2*g^3*(a + b*x))) - (B*i^2*n*(c + d*x)^2)/(4*b*g^3*(a + b*x)^2) - (d*i^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^2*g^3*(a + b*x)) - (i^2*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b*g^3*(a + b*x)^2) - (d^2*i^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3) + (B*d^2*i^2*n*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^4, x, 2, -(B*i^2*n*(c + d*x)^3)/(9*(b*c - a*d)*g^4*(a + b*x)^3) - (i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*(b*c - a*d)*g^4*(a + b*x)^3)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^5, x, 5, (B*d*i^2*n*(c + d*x)^3)/(9*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*B*i^2*n*(c + d*x)^4)/(16*(b*c - a*d)^2*g^5*(a + b*x)^4) + (d*i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*i^2*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*(b*c - a*d)^2*g^5*(a + b*x)^4)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^6, x, 5, -(B*d^2*i^2*n*(c + d*x)^3)/(9*(b*c - a*d)^3*g^6*(a + b*x)^3) + (b*B*d*i^2*n*(c + d*x)^4)/(8*(b*c - a*d)^3*g^6*(a + b*x)^4) - (b^2*B*i^2*n*(c + d*x)^5)/(25*(b*c - a*d)^3*g^6*(a + b*x)^5) - (d^2*i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*(b*c - a*d)^3*g^6*(a + b*x)^3) + (b*d*i^2*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^3*g^6*(a + b*x)^4) - (b^2*i^2*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(5*(b*c - a*d)^3*g^6*(a + b*x)^5)]


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 5, (B*(b*c - a*d)^6*g^3*i^3*n*x)/(140*b^3*d^3) + (B*(b*c - a*d)^5*g^3*i^3*n*(c + d*x)^2)/(280*b^2*d^4) + (B*(b*c - a*d)^4*g^3*i^3*n*(c + d*x)^3)/(420*b*d^4) - (17*B*(b*c - a*d)^3*g^3*i^3*n*(c + d*x)^4)/(280*d^4) + (b*B*(b*c - a*d)^2*g^3*i^3*n*(c + d*x)^5)/(14*d^4) - (b^2*B*(b*c - a*d)*g^3*i^3*n*(c + d*x)^6)/(42*d^4) - ((b*c - a*d)^3*g^3*i^3*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*d^4) + (3*b*(b*c - a*d)^2*g^3*i^3*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(5*d^4) - (b^2*(b*c - a*d)*g^3*i^3*(c + d*x)^6*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d^4) + (b^3*g^3*i^3*(c + d*x)^7*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(7*d^4) + (B*(b*c - a*d)^7*g^3*i^3*n*log((a + b*x)/(c + d*x)))/(140*b^4*d^4) + (B*(b*c - a*d)^7*g^3*i^3*n*log(c + d*x))/(140*b^4*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 5, -((B*(b*c - a*d)^5*g^2*i^3*n*x)/(60*b^3*d^2)) - (B*(b*c - a*d)^4*g^2*i^3*n*(c + d*x)^2)/(120*b^2*d^3) - (B*(b*c - a*d)^3*g^2*i^3*n*(c + d*x)^3)/(180*b*d^3) + (7*B*(b*c - a*d)^2*g^2*i^3*n*(c + d*x)^4)/(120*d^3) - (b*B*(b*c - a*d)*g^2*i^3*n*(c + d*x)^5)/(30*d^3) + ((b*c - a*d)^2*g^2*i^3*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*d^3) - (2*b*(b*c - a*d)*g^2*i^3*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(5*d^3) + (b^2*g^2*i^3*(c + d*x)^6*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(6*d^3) - (B*(b*c - a*d)^6*g^2*i^3*n*log((a + b*x)/(c + d*x)))/(60*b^4*d^3) - (B*(b*c - a*d)^6*g^2*i^3*n*log(c + d*x))/(60*b^4*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 5, (B*(b*c - a*d)^4*g*i^3*n*x)/(20*b^3*d) + (B*(b*c - a*d)^3*g*i^3*n*(c + d*x)^2)/(40*b^2*d^2) + (B*(b*c - a*d)^2*g*i^3*n*(c + d*x)^3)/(60*b*d^2) - (B*(b*c - a*d)*g*i^3*n*(c + d*x)^4)/(20*d^2) - ((b*c - a*d)*g*i^3*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*d^2) + (b*g*i^3*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(5*d^2) + (B*(b*c - a*d)^5*g*i^3*n*log((a + b*x)/(c + d*x)))/(20*b^4*d^2) + (B*(b*c - a*d)^5*g*i^3*n*log(c + d*x))/(20*b^4*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)), x, 4, -(B*(b*c - a*d)^3*i^3*n*x)/(4*b^3) - (B*(b*c - a*d)^2*i^3*n*(c + d*x)^2)/(8*b^2*d) - (B*(b*c - a*d)*i^3*n*(c + d*x)^3)/(12*b*d) - (B*(b*c - a*d)^4*i^3*n*log(a + b*x))/(4*b^4*d) + (i^3*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*d)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^1, x, 14, -((5*B*d*(b*c - a*d)^2*i^3*n*x)/(6*b^3*g)) - (B*(b*c - a*d)*i^3*n*(c + d*x)^2)/(6*b^2*g) + (d*(b*c - a*d)^2*i^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^4*g) + ((b*c - a*d)*i^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b^2*g) + (i^3*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*b*g) - (5*B*(b*c - a*d)^3*i^3*n*log((a + b*x)/(c + d*x)))/(6*b^4*g) - (11*B*(b*c - a*d)^3*i^3*n*log(c + d*x))/(6*b^4*g) - ((b*c - a*d)^3*i^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g) + (B*(b*c - a*d)^3*i^3*n*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^2, x, 11, -((B*d^2*(b*c - a*d)*i^3*n*x)/(2*b^3*g^2)) - (B*(b*c - a*d)^2*i^3*n*(c + d*x))/(b^3*g^2*(a + b*x)) + (2*d^2*(b*c - a*d)*i^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^4*g^2) - ((b*c - a*d)^2*i^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^3*g^2*(a + b*x)) + (d*i^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b^2*g^2) - (B*d*(b*c - a*d)^2*i^3*n*log((a + b*x)/(c + d*x)))/(2*b^4*g^2) - (5*B*d*(b*c - a*d)^2*i^3*n*log(c + d*x))/(2*b^4*g^2) - (3*d*(b*c - a*d)^2*i^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) + (3*B*d*(b*c - a*d)^2*i^3*n*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^3, x, 9, -((2*B*d*(b*c - a*d)*i^3*n*(c + d*x))/(b^3*g^3*(a + b*x))) - (B*(b*c - a*d)*i^3*n*(c + d*x)^2)/(4*b^2*g^3*(a + b*x)^2) + (d^3*i^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^4*g^3) - (2*d*(b*c - a*d)*i^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^3*g^3*(a + b*x)) - ((b*c - a*d)*i^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b^2*g^3*(a + b*x)^2) - (B*d^2*(b*c - a*d)*i^3*n*log(c + d*x))/(b^4*g^3) - (3*d^2*(b*c - a*d)*i^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3) + (3*B*d^2*(b*c - a*d)*i^3*n*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(a*g + b*g*x)^4, x, 9, -((B*d^2*i^3*n*(c + d*x))/(b^3*g^4*(a + b*x))) - (B*d*i^3*n*(c + d*x)^2)/(4*b^2*g^4*(a + b*x)^2) - (B*i^3*n*(c + d*x)^3)/(9*b*g^4*(a + b*x)^3) - (d^2*i^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^3*g^4*(a + b*x)) - (d*i^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b^2*g^4*(a + b*x)^2) - (i^3*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*b*g^4*(a + b*x)^3) - (d^3*i^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^4) + (B*d^3*i^3*n*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^4)]


    #= ::Subsubsection::Closed:: =#
    #=q<0=#


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x), x, 6, (g^3*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*d*i) - ((b*c - a*d)*g^3*(a + b*x)^2*(3*A + B*n + 3*B*log(e*((a + b*x)/(c + d*x))^n)))/(6*d^2*i) + ((b*c - a*d)^2*g^3*(a + b*x)*(6*A + 5*B*n + 6*B*log(e*((a + b*x)/(c + d*x))^n)))/(6*d^3*i) + ((b*c - a*d)^3*g^3*(6*A + 11*B*n + 6*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(6*d^4*i) + (B*(b*c - a*d)^3*g^3*n*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x), x, 5, (g^2*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d*i) - ((b*c - a*d)*g^2*(a + b*x)*(2*A + B*n + 2*B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d^2*i) - ((b*c - a*d)^2*g^2*(2*A + 3*B*n + 2*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(2*d^3*i) - (B*(b*c - a*d)^2*g^2*n*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x), x, 4, (g*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(d*i) + ((b*c - a*d)*g*(A + B*n + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^2*i) + (B*(b*c - a*d)*g*n*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x), x, 5, -(((A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d*i)) - (B*n*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d*i)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^1*(c*i + d*i*x)), x, 2, (A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(2*B*(b*c - a*d)*g*i*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^2*(c*i + d*i*x)), x, 5, -((b*B*n*(c + d*x))/((b*c - a*d)^2*g^2*i*(a + b*x))) - (b*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^2*g^2*i*(a + b*x)) - (d*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^2*g^2*i) + (B*d*n*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^2*g^2*i)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^3*(c*i + d*i*x)), x, 7, -(B*n*(c + d*x)^2*(b - (4*d*(a + b*x))/(c + d*x))^2)/(4*(b*c - a*d)^3*g^3*i*(a + b*x)^2) + (2*b*d*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^3*g^3*i*(a + b*x)) - (b^2*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^3*g^3*i*(a + b*x)^2) + (d^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^3*g^3*i) - (B*d^2*n*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^3*g^3*i)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^4*(c*i + d*i*x)), x, 8, (-3*b*B*d^2*n*(c + d*x))/((b*c - a*d)^4*g^4*i*(a + b*x)) + (3*b^2*B*d*n*(c + d*x)^2)/(4*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (b^3*B*n*(c + d*x)^3)/(9*(b*c - a*d)^4*g^4*i*(a + b*x)^3) - (3*b*d^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^4*g^4*i*(a + b*x)) + (3*b^2*d*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (b^3*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*(b*c - a*d)^4*g^4*i*(a + b*x)^3) - (d^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^4*g^4*i) + (B*d^3*n*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^4*g^4*i)]


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x)^2, x, 9, (3*B*(b*c - a*d)^2*g^3*n*(a + b*x))/(d^3*i^2*(c + d*x)) - ((b*c - a*d)^2*g^3*(6*A + 5*B*n)*(a + b*x))/(2*d^3*i^2*(c + d*x)) - (3*B*(b*c - a*d)^2*g^3*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d^3*i^2*(c + d*x)) + (g^3*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d*i^2*(c + d*x)) - ((b*c - a*d)*g^3*(a + b*x)^2*(3*A + B*n + 3*B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d^2*i^2*(c + d*x)) - (b*(b*c - a*d)^2*g^3*(6*A + 5*B*n + 6*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(2*d^4*i^2) - (3*b*B*(b*c - a*d)^2*g^3*n*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^2)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x)^2, x, 8, (-2*B*(b*c - a*d)*g^2*n*(a + b*x))/(d^2*i^2*(c + d*x)) + ((b*c - a*d)*g^2*(2*A + B*n)*(a + b*x))/(d^2*i^2*(c + d*x)) + (2*B*(b*c - a*d)*g^2*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d^2*i^2*(c + d*x)) + (g^2*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(d*i^2*(c + d*x)) + (b*(b*c - a*d)*g^2*(2*A + B*n + 2*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^3*i^2) + (2*b*B*(b*c - a*d)*g^2*n*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^2)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x)^2, x, 7, -((A*g*(a + b*x))/(d*i^2*(c + d*x))) + (B*g*n*(a + b*x))/(d*i^2*(c + d*x)) - (B*g*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d*i^2*(c + d*x)) - (b*g*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^2*i^2) - (b*B*g*n*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i^2)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x)^2, x, 3, (A*(a + b*x))/((b*c - a*d)*i^2*(c + d*x)) - (B*n*(a + b*x))/((b*c - a*d)*i^2*(c + d*x)) + (B*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)*i^2*(c + d*x))]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^1*(c*i + d*i*x)^2), x, 5, -((A*d*(a + b*x))/((b*c - a*d)^2*g*i^2*(c + d*x))) + (B*d*n*(a + b*x))/((b*c - a*d)^2*g*i^2*(c + d*x)) - (B*d*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^2*g*i^2*(c + d*x)) + (b*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*B*(b*c - a*d)^2*g*i^2*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^2*(c*i + d*i*x)^2), x, 4, -((B*d^2*n*(a + b*x))/((b*c - a*d)^3*g^2*i^2*(c + d*x))) - (b^2*B*n*(c + d*x))/((b*c - a*d)^3*g^2*i^2*(a + b*x)) + (d^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^3*g^2*i^2*(c + d*x)) - (b^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^3*g^2*i^2*(a + b*x)) - (2*b*d*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^3*g^2*i^2) + (b*B*d*n*log((a + b*x)/(c + d*x))^2)/((b*c - a*d)^3*g^2*i^2)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^3*(c*i + d*i*x)^2), x, 8, (B*d^3*n*(a + b*x))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (3*b^2*B*d*n*(c + d*x))/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*B*n*(c + d*x)^2)/(4*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) - (d^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (3*b^2*d*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) + (3*b*d^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^4*g^3*i^2) - (3*b*B*d^2*n*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^4*g^3*i^2)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^4*(c*i + d*i*x)^2), x, 4, -((B*d^4*n*(a + b*x))/((b*c - a*d)^5*g^4*i^2*(c + d*x))) - (6*b^2*B*d^2*n*(c + d*x))/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (b^3*B*d*n*(c + d*x)^2)/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (b^4*B*n*(c + d*x)^3)/(9*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) + (d^4*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^5*g^4*i^2*(c + d*x)) - (6*b^2*d^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (2*b^3*d*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (b^4*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) - (4*b*d^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^5*g^4*i^2) + (2*b*B*d^3*n*log((a + b*x)/(c + d*x))^2)/((b*c - a*d)^5*g^4*i^2)]


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x)^3, x, 9, (-3*B*(b*c - a*d)*g^3*n*(a + b*x)^2)/(4*d^2*i^3*(c + d*x)^2) - (3*b*B*(b*c - a*d)*g^3*n*(a + b*x))/(d^3*i^3*(c + d*x)) + (b*(b*c - a*d)*g^3*(3*A + B*n)*(a + b*x))/(d^3*i^3*(c + d*x)) + (3*b*B*(b*c - a*d)*g^3*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d^3*i^3*(c + d*x)) + (g^3*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(d*i^3*(c + d*x)^2) + ((b*c - a*d)*g^3*(a + b*x)^2*(3*A + B*n + 3*B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d^2*i^3*(c + d*x)^2) + (b^2*(b*c - a*d)*g^3*(3*A + B*n + 3*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^4*i^3) + (3*b^2*B*(b*c - a*d)*g^3*n*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^3)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x)^3, x, 8, (B*g^2*n*(a + b*x)^2)/(4*d*i^3*(c + d*x)^2) - (A*b*g^2*(a + b*x))/(d^2*i^3*(c + d*x)) + (b*B*g^2*n*(a + b*x))/(d^2*i^3*(c + d*x)) - (b*B*g^2*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d^2*i^3*(c + d*x)) - (g^2*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d*i^3*(c + d*x)^2) - (b^2*g^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^3*i^3) - (b^2*B*g^2*n*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^3)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x)^3, x, 2, -(B*g*n*(a + b*x)^2)/(4*(b*c - a*d)*i^3*(c + d*x)^2) + (g*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)*i^3*(c + d*x)^2)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*((a + b*x)/(c + d*x))^n))/(c*i + d*i*x)^3, x, 4, (B*n)/(4*d*i^3*(c + d*x)^2) + (b*B*n)/(2*d*(b*c - a*d)*i^3*(c + d*x)) + (b^2*B*n*log(a + b*x))/(2*d*(b*c - a*d)^2*i^3) - (A + B*log(e*((a + b*x)/(c + d*x))^n))/(2*d*i^3*(c + d*x)^2) - (b^2*B*n*log(c + d*x))/(2*d*(b*c - a*d)^2*i^3)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^1*(c*i + d*i*x)^3), x, 4, -(B*n*(4*b - (d*(a + b*x))/(c + d*x))^2)/(4*(b*c - a*d)^3*g*i^3) + (d^2*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^3*g*i^3*(c + d*x)^2) - (2*b*d*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^3*g*i^3*(c + d*x)) + (b^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^3*g*i^3) - (b^2*B*n*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^3*g*i^3)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^2*(c*i + d*i*x)^3), x, 4, (B*d^3*n*(a + b*x)^2)/(4*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2) - (3*b*B*d^2*n*(a + b*x))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) - (b^3*B*n*(c + d*x))/((b*c - a*d)^4*g^2*i^3*(a + b*x)) - (d^3*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2) + (3*b*d^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) - (b^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^4*g^2*i^3*(a + b*x)) - (3*b^2*d*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^4*g^2*i^3) + (3*b^2*B*d*n*log((a + b*x)/(c + d*x))^2)/(2*(b*c - a*d)^4*g^2*i^3)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^3*(c*i + d*i*x)^3), x, 5, -(B*d^4*n*(a + b*x)^2)/(4*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2) + (4*b*B*d^3*n*(a + b*x))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) + (4*b^3*B*d*n*(c + d*x))/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*B*n*(c + d*x)^2)/(4*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) + (d^4*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2) - (4*b*d^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) + (4*b^3*d*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) + (6*b^2*d^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^5*g^3*i^3) - (3*b^2*B*d^2*n*log((a + b*x)/(c + d*x))^2)/((b*c - a*d)^5*g^3*i^3)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))/((a*g + b*g*x)^4*(c*i + d*i*x)^3), x, 8, (B*d^5*n*(a + b*x)^2)/(4*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2) - (5*b*B*d^4*n*(a + b*x))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) - (10*b^3*B*d^2*n*(c + d*x))/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*B*d*n*(c + d*x)^2)/(4*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (b^5*B*n*(c + d*x)^3)/(9*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) - (d^5*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2) + (5*b*d^4*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) - (10*b^3*d^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*d*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (b^5*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) - (10*b^2*d^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((a + b*x)/(c + d*x)))/((b*c - a*d)^6*g^4*i^3) + (5*b^2*B*d^3*n*log((a + b*x)/(c + d*x))^2)/((b*c - a*d)^6*g^4*i^3)]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*((a+b*x) / (c+d*x))^n))^2*when*b*f-a*g=0*and*d*h-c*i=0=#


    #= ::Subsubsection::Closed:: =#
    #=q>0=#


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 11, (3*B^2*(b*c - a*d)^4*g^3*i*n^2*x)/(10*b*d^3) - (3*B^2*(b*c - a*d)^3*g^3*i*n^2*(c + d*x)^2)/(20*d^4) + (b*B^2*(b*c - a*d)^2*g^3*i*n^2*(c + d*x)^3)/(30*d^4) - (B*(b*c - a*d)^2*g^3*i*n*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(30*b^2*d) - (B*(b*c - a*d)*g^3*i*n*(a + b*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(10*b^2) + ((b*c - a*d)*g^3*i*(a + b*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(20*b^2) + (g^3*i*(a + b*x)^4*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(5*b) + (B*(b*c - a*d)^3*g^3*i*n*(a + b*x)^2*(3*A + B*n + 3*B*log(e*((a + b*x)/(c + d*x))^n)))/(60*b^2*d^2) - (B*(b*c - a*d)^4*g^3*i*n*(a + b*x)*(6*A + 5*B*n + 6*B*log(e*((a + b*x)/(c + d*x))^n)))/(60*b^2*d^3) - (B*(b*c - a*d)^5*g^3*i*n*(6*A + 11*B*n + 6*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(60*b^2*d^4) - (B^2*(b*c - a*d)^5*g^3*i*n^2*log(c + d*x))/(10*b^2*d^4) - (B^2*(b*c - a*d)^5*g^3*i*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(10*b^2*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 10, -(B^2*(b*c - a*d)^3*g^2*i*n^2*x)/(3*b*d^2) + (B^2*(b*c - a*d)^2*g^2*i*n^2*(c + d*x)^2)/(12*d^3) - (B*(b*c - a*d)^2*g^2*i*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(12*b^2*d) - (B*(b*c - a*d)*g^2*i*n*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(6*b^2) + ((b*c - a*d)*g^2*i*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(12*b^2) + (g^2*i*(a + b*x)^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(4*b) + (B*(b*c - a*d)^3*g^2*i*n*(a + b*x)*(2*A + B*n + 2*B*log(e*((a + b*x)/(c + d*x))^n)))/(12*b^2*d^2) + (B*(b*c - a*d)^4*g^2*i*n*(2*A + 3*B*n + 2*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(12*b^2*d^3) + (B^2*(b*c - a*d)^4*g^2*i*n^2*log(c + d*x))/(6*b^2*d^3) + (B^2*(b*c - a*d)^4*g^2*i*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(6*b^2*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 9, (B^2*(b*c - a*d)^2*g*i*n^2*x)/(3*b*d) - (B*(b*c - a*d)^2*g*i*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*b^2*d) - (B*(b*c - a*d)*g*i*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*b^2) + ((b*c - a*d)*g*i*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(6*b^2) + (g*i*(a + b*x)^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*b) - (B*(b*c - a*d)^3*g*i*n*(A + B*n + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(3*b^2*d^2) - (B^2*(b*c - a*d)^3*g*i*n^2*log(c + d*x))/(3*b^2*d^2) - (B^2*(b*c - a*d)^3*g*i*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(3*b^2*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 7, -((B*(b*c - a*d)*i*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/b^2) + (i*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*d) + (B^2*(b*c - a*d)^2*i*n^2*log(c + d*x))/(b^2*d) + (B*(b*c - a*d)^2*i*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^2*d) - (B^2*(b*c - a*d)^2*i*n^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^2*d)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^1, x, 8, (d*i*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^2*g) + (2*B*(b*c - a*d)*i*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(b^2*g) - ((b*c - a*d)*i*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^2*g) + (2*B^2*(b*c - a*d)*i*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^2*g) + (2*B*(b*c - a*d)*i*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g) + (2*B^2*(b*c - a*d)*i*n^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^2, x, 7, -((2*B^2*i*n^2*(c + d*x))/(b*g^2*(a + b*x))) - (2*B*i*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b*g^2*(a + b*x)) - (i*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b*g^2*(a + b*x)) - (d*i*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2) + (2*B*d*i*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2) + (2*B^2*d*i*n^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^2*g^2)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^3, x, 3, -(B^2*i*n^2*(c + d*x)^2)/(4*(b*c - a*d)*g^3*(a + b*x)^2) - (B*i*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)*g^3*(a + b*x)^2) - (i*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)*g^3*(a + b*x)^2)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^4, x, 7, (B^2*d*i*n^2*(c + d*x)^2)/(4*(b*c - a*d)^2*g^4*(a + b*x)^2) - (2*b*B^2*i*n^2*(c + d*x)^3)/(27*(b*c - a*d)^2*g^4*(a + b*x)^3) + (B*d*i*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^2*g^4*(a + b*x)^2) - (2*b*B*i*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(9*(b*c - a*d)^2*g^4*(a + b*x)^3) + (d*i*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^2*g^4*(a + b*x)^2) - (b*i*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*(b*c - a*d)^2*g^4*(a + b*x)^3)]
    @test_int [(c*i + d*i*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^5, x, 9, -(B^2*d^2*i*n^2*(c + d*x)^2)/(4*(b*c - a*d)^3*g^5*(a + b*x)^2) + (4*b*B^2*d*i*n^2*(c + d*x)^3)/(27*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*B^2*i*n^2*(c + d*x)^4)/(32*(b*c - a*d)^3*g^5*(a + b*x)^4) - (B*d^2*i*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^3*g^5*(a + b*x)^2) + (4*b*B*d*i*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(9*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*B*i*n*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(8*(b*c - a*d)^3*g^5*(a + b*x)^4) - (d^2*i*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^3*g^5*(a + b*x)^2) + (2*b*d*i*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*(b*c - a*d)^3*g^5*(a + b*x)^3) - (b^2*i*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(4*(b*c - a*d)^3*g^5*(a + b*x)^4)]


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 17, (3*B^2*(b*c - a*d)^5*g^3*i^2*n^2*x)/(20*b^2*d^3) + (B^2*(b*c - a*d)^2*g^3*i^2*n^2*(a + b*x)^4)/(60*b^3) - (3*B^2*(b*c - a*d)^4*g^3*i^2*n^2*(c + d*x)^2)/(40*b*d^4) + (B^2*(b*c - a*d)^3*g^3*i^2*n^2*(c + d*x)^3)/(60*d^4) - (B*(b*c - a*d)^3*g^3*i^2*n*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(90*b^3*d) - (B*(b*c - a*d)^2*g^3*i^2*n*(a + b*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(20*b^3) - (B*(b*c - a*d)*g^3*i^2*n*(a + b*x)^4*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(15*b^2) + ((b*c - a*d)^2*g^3*i^2*(a + b*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(60*b^3) + ((b*c - a*d)*g^3*i^2*(a + b*x)^4*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(15*b^2) + (g^3*i^2*(a + b*x)^4*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(6*b) + (B*(b*c - a*d)^4*g^3*i^2*n*(a + b*x)^2*(3*A + B*n + 3*B*log(e*((a + b*x)/(c + d*x))^n)))/(180*b^3*d^2) - (B*(b*c - a*d)^5*g^3*i^2*n*(a + b*x)*(6*A + 5*B*n + 6*B*log(e*((a + b*x)/(c + d*x))^n)))/(180*b^3*d^3) - (B*(b*c - a*d)^6*g^3*i^2*n*(6*A + 11*B*n + 6*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(180*b^3*d^4) - (B^2*(b*c - a*d)^6*g^3*i^2*n^2*log(c + d*x))/(20*b^3*d^4) - (B^2*(b*c - a*d)^6*g^3*i^2*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(30*b^3*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 15, -(B^2*(b*c - a*d)^4*g^2*i^2*n^2*x)/(10*b^2*d^2) - (B^2*(b*c - a*d)^3*g^2*i^2*n^2*(c + d*x)^2)/(20*b*d^3) + (B^2*(b*c - a*d)^2*g^2*i^2*n^2*(c + d*x)^3)/(30*d^3) - (B*(b*c - a*d)^3*g^2*i^2*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(30*b^3*d) - (B*(b*c - a*d)^2*g^2*i^2*n*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(15*b^3) - (B*(b*c - a*d)^3*g^2*i^2*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(5*b*d^3) + (4*B*(b*c - a*d)^2*g^2*i^2*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(15*d^3) - (b*B*(b*c - a*d)*g^2*i^2*n*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(10*d^3) + ((b*c - a*d)^2*g^2*i^2*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(30*b^3) + ((b*c - a*d)*g^2*i^2*(a + b*x)^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(10*b^2) + (g^2*i^2*(a + b*x)^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(5*b) + (B*(b*c - a*d)^4*g^2*i^2*n*(a + b*x)*(2*A + B*n + 2*B*log(e*((a + b*x)/(c + d*x))^n)))/(30*b^3*d^2) + (B*(b*c - a*d)^5*g^2*i^2*n*(2*A + 3*B*n + 2*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(30*b^3*d^3) + (B^2*(b*c - a*d)^5*g^2*i^2*n^2*log((a + b*x)/(c + d*x)))/(30*b^3*d^3) + (B^2*(b*c - a*d)^5*g^2*i^2*n^2*log(c + d*x))/(10*b^3*d^3) + (B^2*(b*c - a*d)^5*g^2*i^2*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(15*b^3*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 14, (B^2*(b*c - a*d)^3*g*i^2*n^2*x)/(12*b^2*d) + (B^2*(b*c - a*d)^2*g*i^2*n^2*(c + d*x)^2)/(12*b*d^2) - (B*(b*c - a*d)^3*g*i^2*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(6*b^3*d) - (B*(b*c - a*d)^2*g*i^2*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(6*b^3) + (B*(b*c - a*d)^2*g*i^2*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*b*d^2) - (B*(b*c - a*d)*g*i^2*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(6*d^2) + ((b*c - a*d)^2*g*i^2*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(12*b^3) + ((b*c - a*d)*g*i^2*(a + b*x)^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(6*b^2) + (g*i^2*(a + b*x)^2*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(4*b) - (B*(b*c - a*d)^4*g*i^2*n*(A + B*n + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(6*b^3*d^2) - (B^2*(b*c - a*d)^4*g*i^2*n^2*log((a + b*x)/(c + d*x)))/(12*b^3*d^2) - (B^2*(b*c - a*d)^4*g*i^2*n^2*log(c + d*x))/(4*b^3*d^2) - (B^2*(b*c - a*d)^4*g*i^2*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(6*b^3*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 11, (B^2*(b*c - a*d)^2*i^2*n^2*x)/(3*b^2) - (2*B*(b*c - a*d)^2*i^2*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*b^3) - (B*(b*c - a*d)*i^2*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*b*d) + (i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*d) + (B^2*(b*c - a*d)^3*i^2*n^2*log((a + b*x)/(c + d*x)))/(3*b^3*d) + (B^2*(b*c - a*d)^3*i^2*n^2*log(c + d*x))/(b^3*d) + (2*B*(b*c - a*d)^3*i^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(3*b^3*d) - (2*B^2*(b*c - a*d)^3*i^2*n^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(3*b^3*d)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^1, x, 15, -((B*d*(b*c - a*d)*i^2*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^3*g)) + (d*(b*c - a*d)*i^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^3*g) + (i^2*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*b*g) + (2*B*(b*c - a*d)^2*i^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(b^3*g) + (B^2*(b*c - a*d)^2*i^2*n^2*log(c + d*x))/(b^3*g) + (B*(b*c - a*d)^2*i^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) - ((b*c - a*d)^2*i^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) + (2*B^2*(b*c - a*d)^2*i^2*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^3*g) - (B^2*(b*c - a*d)^2*i^2*n^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) + (2*B*(b*c - a*d)^2*i^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g) + (2*B^2*(b*c - a*d)^2*i^2*n^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^2, x, 11, -((2*B^2*(b*c - a*d)*i^2*n^2*(c + d*x))/(b^2*g^2*(a + b*x))) - (2*B*(b*c - a*d)*i^2*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^2*g^2*(a + b*x)) + (d^2*i^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^3*g^2) - ((b*c - a*d)*i^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^2*g^2*(a + b*x)) + (2*B*d*(b*c - a*d)*i^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(b^3*g^2) - (2*d*(b*c - a*d)*i^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2) + (2*B^2*d*(b*c - a*d)*i^2*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^3*g^2) + (4*B*d*(b*c - a*d)*i^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2) + (4*B^2*d*(b*c - a*d)*i^2*n^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^2)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^3, x, 10, -((2*B^2*d*i^2*n^2*(c + d*x))/(b^2*g^3*(a + b*x))) - (B^2*i^2*n^2*(c + d*x)^2)/(4*b*g^3*(a + b*x)^2) - (2*B*d*i^2*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^2*g^3*(a + b*x)) - (B*i^2*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b*g^3*(a + b*x)^2) - (d*i^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^2*g^3*(a + b*x)) - (i^2*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*b*g^3*(a + b*x)^2) - (d^2*i^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3) + (2*B*d^2*i^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3) + (2*B^2*d^2*i^2*n^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^3*g^3)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^4, x, 3, (-2*B^2*i^2*n^2*(c + d*x)^3)/(27*(b*c - a*d)*g^4*(a + b*x)^3) - (2*B*i^2*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(9*(b*c - a*d)*g^4*(a + b*x)^3) - (i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*(b*c - a*d)*g^4*(a + b*x)^3)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^5, x, 7, (2*B^2*d*i^2*n^2*(c + d*x)^3)/(27*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*B^2*i^2*n^2*(c + d*x)^4)/(32*(b*c - a*d)^2*g^5*(a + b*x)^4) + (2*B*d*i^2*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(9*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*B*i^2*n*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(8*(b*c - a*d)^2*g^5*(a + b*x)^4) + (d*i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*(b*c - a*d)^2*g^5*(a + b*x)^3) - (b*i^2*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(4*(b*c - a*d)^2*g^5*(a + b*x)^4)]
    @test_int [(c*i + d*i*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^6, x, 9, (-2*B^2*d^2*i^2*n^2*(c + d*x)^3)/(27*(b*c - a*d)^3*g^6*(a + b*x)^3) + (b*B^2*d*i^2*n^2*(c + d*x)^4)/(16*(b*c - a*d)^3*g^6*(a + b*x)^4) - (2*b^2*B^2*i^2*n^2*(c + d*x)^5)/(125*(b*c - a*d)^3*g^6*(a + b*x)^5) - (2*B*d^2*i^2*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(9*(b*c - a*d)^3*g^6*(a + b*x)^3) + (b*B*d*i^2*n*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*(b*c - a*d)^3*g^6*(a + b*x)^4) - (2*b^2*B*i^2*n*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(25*(b*c - a*d)^3*g^6*(a + b*x)^5) - (d^2*i^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*(b*c - a*d)^3*g^6*(a + b*x)^3) + (b*d*i^2*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^3*g^6*(a + b*x)^4) - (b^2*i^2*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(5*(b*c - a*d)^3*g^6*(a + b*x)^5)]


    @test_int [(a*g + b*g*x)^3*(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 22, (5*B^2*(b*c - a*d)^6*g^3*i^3*n^2*x)/(84*b^3*d^3) + (B^2*(b*c - a*d)^3*g^3*i^3*n^2*(a + b*x)^4)/(140*b^4) - (29*B^2*(b*c - a*d)^5*g^3*i^3*n^2*(c + d*x)^2)/(840*b^2*d^4) + (47*B^2*(b*c - a*d)^4*g^3*i^3*n^2*(c + d*x)^3)/(1260*b*d^4) - (13*B^2*(b*c - a*d)^3*g^3*i^3*n^2*(c + d*x)^4)/(420*d^4) + (b*B^2*(b*c - a*d)^2*g^3*i^3*n^2*(c + d*x)^5)/(105*d^4) - (B*(b*c - a*d)^4*g^3*i^3*n*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(210*b^4*d) - (3*B*(b*c - a*d)^3*g^3*i^3*n*(a + b*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(140*b^4) - (B*(b*c - a*d)^2*g^3*i^3*n*(a + b*x)^4*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(35*b^3) + (2*B*(b*c - a*d)^4*g^3*i^3*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(21*b*d^4) - (3*B*(b*c - a*d)^3*g^3*i^3*n*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(14*d^4) + (6*b*B*(b*c - a*d)^2*g^3*i^3*n*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(35*d^4) - (b^2*B*(b*c - a*d)*g^3*i^3*n*(c + d*x)^6*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(21*d^4) + ((b*c - a*d)^3*g^3*i^3*(a + b*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(140*b^4) + ((b*c - a*d)^2*g^3*i^3*(a + b*x)^4*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(35*b^3) + ((b*c - a*d)*g^3*i^3*(a + b*x)^4*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(14*b^2) + (g^3*i^3*(a + b*x)^4*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(7*b) + (B*(b*c - a*d)^5*g^3*i^3*n*(a + b*x)^2*(3*A + B*n + 3*B*log(e*((a + b*x)/(c + d*x))^n)))/(420*b^4*d^2) - (B*(b*c - a*d)^6*g^3*i^3*n*(a + b*x)*(6*A + 5*B*n + 6*B*log(e*((a + b*x)/(c + d*x))^n)))/(420*b^4*d^3) - (B*(b*c - a*d)^7*g^3*i^3*n*(6*A + 11*B*n + 6*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(420*b^4*d^4) - (B^2*(b*c - a*d)^7*g^3*i^3*n^2*log((a + b*x)/(c + d*x)))/(210*b^4*d^4) - (11*B^2*(b*c - a*d)^7*g^3*i^3*n^2*log(c + d*x))/(420*b^4*d^4) - (B^2*(b*c - a*d)^7*g^3*i^3*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(70*b^4*d^4)]
    @test_int [(a*g + b*g*x)^2*(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 20, (-7*B^2*(b*c - a*d)^5*g^2*i^3*n^2*x)/(180*b^3*d^2) - (7*B^2*(b*c - a*d)^4*g^2*i^3*n^2*(c + d*x)^2)/(360*b^2*d^3) - (B^2*(b*c - a*d)^3*g^2*i^3*n^2*(c + d*x)^3)/(60*b*d^3) + (B^2*(b*c - a*d)^2*g^2*i^3*n^2*(c + d*x)^4)/(60*d^3) - (B*(b*c - a*d)^4*g^2*i^3*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(60*b^4*d) - (B*(b*c - a*d)^3*g^2*i^3*n*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(30*b^4) - (B*(b*c - a*d)^4*g^2*i^3*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(10*b^2*d^3) + (B*(b*c - a*d)^3*g^2*i^3*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(45*b*d^3) + (7*B*(b*c - a*d)^2*g^2*i^3*n*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(60*d^3) - (b*B*(b*c - a*d)*g^2*i^3*n*(c + d*x)^5*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(15*d^3) + ((b*c - a*d)^3*g^2*i^3*(a + b*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(60*b^4) + ((b*c - a*d)^2*g^2*i^3*(a + b*x)^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(20*b^3) + ((b*c - a*d)*g^2*i^3*(a + b*x)^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(10*b^2) + (g^2*i^3*(a + b*x)^3*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(6*b) + (B*(b*c - a*d)^5*g^2*i^3*n*(a + b*x)*(2*A + B*n + 2*B*log(e*((a + b*x)/(c + d*x))^n)))/(60*b^4*d^2) + (B*(b*c - a*d)^6*g^2*i^3*n*(2*A + 3*B*n + 2*B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(60*b^4*d^3) + (B^2*(b*c - a*d)^6*g^2*i^3*n^2*log((a + b*x)/(c + d*x)))/(36*b^4*d^3) + (11*B^2*(b*c - a*d)^6*g^2*i^3*n^2*log(c + d*x))/(180*b^4*d^3) + (B^2*(b*c - a*d)^6*g^2*i^3*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(30*b^4*d^3)]
    @test_int [(a*g + b*g*x)^1*(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 19, (B^2*(b*c - a*d)^4*g*i^3*n^2*x)/(60*b^3*d) + (B^2*(b*c - a*d)^3*g*i^3*n^2*(c + d*x)^2)/(30*b^2*d^2) + (B^2*(b*c - a*d)^2*g*i^3*n^2*(c + d*x)^3)/(30*b*d^2) - (B*(b*c - a*d)^4*g*i^3*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(10*b^4*d) - (B*(b*c - a*d)^3*g*i^3*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(10*b^4) + (3*B*(b*c - a*d)^3*g*i^3*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(20*b^2*d^2) + (B*(b*c - a*d)^2*g*i^3*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(30*b*d^2) - (B*(b*c - a*d)*g*i^3*n*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(10*d^2) + ((b*c - a*d)^3*g*i^3*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(20*b^4) + ((b*c - a*d)^2*g*i^3*(a + b*x)^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(10*b^3) + (3*(b*c - a*d)*g*i^3*(a + b*x)^2*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(20*b^2) + (g*i^3*(a + b*x)^2*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(5*b) - (B*(b*c - a*d)^5*g*i^3*n*(A + B*n + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(10*b^4*d^2) - (B^2*(b*c - a*d)^5*g*i^3*n^2*log((a + b*x)/(c + d*x)))/(12*b^4*d^2) - (11*B^2*(b*c - a*d)^5*g*i^3*n^2*log(c + d*x))/(60*b^4*d^2) - (B^2*(b*c - a*d)^5*g*i^3*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(10*b^4*d^2)]
    @test_int [(a*g + b*g*x)^0*(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2, x, 15, (5*B^2*(b*c - a*d)^3*i^3*n^2*x)/(12*b^3) + (B^2*(b*c - a*d)^2*i^3*n^2*(c + d*x)^2)/(12*b^2*d) - (B*(b*c - a*d)^3*i^3*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b^4) - (B*(b*c - a*d)^2*i^3*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(4*b^2*d) - (B*(b*c - a*d)*i^3*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(6*b*d) + (i^3*(c + d*x)^4*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(4*d) + (5*B^2*(b*c - a*d)^4*i^3*n^2*log((a + b*x)/(c + d*x)))/(12*b^4*d) + (11*B^2*(b*c - a*d)^4*i^3*n^2*log(c + d*x))/(12*b^4*d) + (B*(b*c - a*d)^4*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(2*b^4*d) - (B^2*(b*c - a*d)^4*i^3*n^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(2*b^4*d)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^1, x, 26, (B^2*d*(b*c - a*d)^2*i^3*n^2*x)/(3*b^3*g) - (5*B*d*(b*c - a*d)^2*i^3*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*b^4*g) - (B*(b*c - a*d)*i^3*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*b^2*g) + (d*(b*c - a*d)^2*i^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^4*g) + ((b*c - a*d)*i^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*b^2*g) + (i^3*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*b*g) + (2*B*(b*c - a*d)^3*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(b^4*g) + (B^2*(b*c - a*d)^3*i^3*n^2*log((a + b*x)/(c + d*x)))/(3*b^4*g) + (2*B^2*(b*c - a*d)^3*i^3*n^2*log(c + d*x))/(b^4*g) + (5*B*(b*c - a*d)^3*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(3*b^4*g) - ((b*c - a*d)^3*i^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g) + (2*B^2*(b*c - a*d)^3*i^3*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^4*g) - (5*B^2*(b*c - a*d)^3*i^3*n^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(3*b^4*g) + (2*B*(b*c - a*d)^3*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g) + (2*B^2*(b*c - a*d)^3*i^3*n^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^2, x, 17, -((2*B^2*(b*c - a*d)^2*i^3*n^2*(c + d*x))/(b^3*g^2*(a + b*x))) - (B*d^2*(b*c - a*d)*i^3*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^4*g^2) - (2*B*(b*c - a*d)^2*i^3*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^3*g^2*(a + b*x)) + (2*d^2*(b*c - a*d)*i^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^4*g^2) - ((b*c - a*d)^2*i^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^3*g^2*(a + b*x)) + (d*i^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*b^2*g^2) + (4*B*d*(b*c - a*d)^2*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(b^4*g^2) + (B^2*d*(b*c - a*d)^2*i^3*n^2*log(c + d*x))/(b^4*g^2) + (B*d*(b*c - a*d)^2*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) - (3*d*(b*c - a*d)^2*i^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) + (4*B^2*d*(b*c - a*d)^2*i^3*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^4*g^2) - (B^2*d*(b*c - a*d)^2*i^3*n^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) + (6*B*d*(b*c - a*d)^2*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2) + (6*B^2*d*(b*c - a*d)^2*i^3*n^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^2)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^3, x, 13, -((4*B^2*d*(b*c - a*d)*i^3*n^2*(c + d*x))/(b^3*g^3*(a + b*x))) - (B^2*(b*c - a*d)*i^3*n^2*(c + d*x)^2)/(4*b^2*g^3*(a + b*x)^2) - (4*B*d*(b*c - a*d)*i^3*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^3*g^3*(a + b*x)) - (B*(b*c - a*d)*i^3*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b^2*g^3*(a + b*x)^2) + (d^3*i^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^4*g^3) - (2*d*(b*c - a*d)*i^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^3*g^3*(a + b*x)) - ((b*c - a*d)*i^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*b^2*g^3*(a + b*x)^2) + (2*B*d^2*(b*c - a*d)*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(b^4*g^3) - (3*d^2*(b*c - a*d)*i^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3) + (2*B^2*d^2*(b*c - a*d)*i^3*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(b^4*g^3) + (6*B*d^2*(b*c - a*d)*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3) + (6*B^2*d^2*(b*c - a*d)*i^3*n^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^3)]
    @test_int [(c*i + d*i*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^4, x, 13, -((2*B^2*d^2*i^3*n^2*(c + d*x))/(b^3*g^4*(a + b*x))) - (B^2*d*i^3*n^2*(c + d*x)^2)/(4*b^2*g^4*(a + b*x)^2) - (2*B^2*i^3*n^2*(c + d*x)^3)/(27*b*g^4*(a + b*x)^3) - (2*B*d^2*i^3*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(b^3*g^4*(a + b*x)) - (B*d*i^3*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*b^2*g^4*(a + b*x)^2) - (2*B*i^3*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(9*b*g^4*(a + b*x)^3) - (d^2*i^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(b^3*g^4*(a + b*x)) - (d*i^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*b^2*g^4*(a + b*x)^2) - (i^3*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*b*g^4*(a + b*x)^3) - (d^3*i^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^4) + (2*B*d^3*i^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^4) + (2*B^2*d^3*i^3*n^2*PolyLog(3, (b*(c + d*x))/(d*(a + b*x))))/(b^4*g^4)]


    #= ::Subsubsection::Closed:: =#
    #=q<0=#


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x), x, 25, (b*B^2*(b*c - a*d)^2*g^3*n^2*x)/(3*d^3*i) + (7*B*(b*c - a*d)^2*g^3*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*d^3*i) - (b^2*B*(b*c - a*d)*g^3*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(3*d^4*i) + (3*(b*c - a*d)^2*g^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d^3*i) - (3*b^2*(b*c - a*d)*g^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*d^4*i) + (b^3*g^3*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*d^4*i) + (6*B*(b*c - a*d)^3*g^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^4*i) + ((b*c - a*d)^3*g^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log((b*c - a*d)/(b*(c + d*x))))/(d^4*i) + (B^2*(b*c - a*d)^3*g^3*n^2*log((a + b*x)/(c + d*x)))/(3*d^4*i) - (2*B^2*(b*c - a*d)^3*g^3*n^2*log(c + d*x))/(d^4*i) - (7*B*(b*c - a*d)^3*g^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(3*d^4*i) + (6*B^2*(b*c - a*d)^3*g^3*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i) + (2*B*(b*c - a*d)^3*g^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i) + (7*B^2*(b*c - a*d)^3*g^3*n^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(3*d^4*i) - (2*B^2*(b*c - a*d)^3*g^3*n^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x), x, 15, -((B*(b*c - a*d)*g^2*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(d^2*i)) - (2*(b*c - a*d)*g^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d^2*i) + (b^2*g^2*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*d^3*i) - (4*B*(b*c - a*d)^2*g^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^3*i) - ((b*c - a*d)^2*g^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log((b*c - a*d)/(b*(c + d*x))))/(d^3*i) + (B^2*(b*c - a*d)^2*g^2*n^2*log(c + d*x))/(d^3*i) + (B*(b*c - a*d)^2*g^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(d^3*i) - (4*B^2*(b*c - a*d)^2*g^2*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i) - (2*B*(b*c - a*d)^2*g^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i) - (B^2*(b*c - a*d)^2*g^2*n^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(d^3*i) + (2*B^2*(b*c - a*d)^2*g^2*n^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x), x, 9, (g*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d*i) + (2*B*(b*c - a*d)*g*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^2*i) + ((b*c - a*d)*g*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log((b*c - a*d)/(b*(c + d*x))))/(d^2*i) + (2*B^2*(b*c - a*d)*g*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i) + (2*B*(b*c - a*d)*g*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i) - (2*B^2*(b*c - a*d)*g*n^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x), x, 4, -(((A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log((b*c - a*d)/(b*(c + d*x))))/(d*i)) - (2*B*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d*i) + (2*B^2*n^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d*i)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^1*(c*i + d*i*x)), x, 3, (A + B*log(e*((a + b*x)/(c + d*x))^n))^3/(3*B*(b*c - a*d)*g*i*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^2*(c*i + d*i*x)), x, 7, (-2*b*B^2*n^2*(c + d*x))/((b*c - a*d)^2*g^2*i*(a + b*x)) - (2*b*B*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^2*g^2*i*(a + b*x)) - (b*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^2*g^2*i*(a + b*x)) - (d*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(3*B*(b*c - a*d)^2*g^2*i*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^3*(c*i + d*i*x)), x, 9, (4*b*B^2*d*n^2*(c + d*x))/((b*c - a*d)^3*g^3*i*(a + b*x)) - (b^2*B^2*n^2*(c + d*x)^2)/(4*(b*c - a*d)^3*g^3*i*(a + b*x)^2) + (4*b*B*d*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^3*g^3*i*(a + b*x)) - (b^2*B*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^3*g^3*i*(a + b*x)^2) + (2*b*d*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^3*g^3*i*(a + b*x)) - (b^2*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^3*g^3*i*(a + b*x)^2) + (d^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(3*B*(b*c - a*d)^3*g^3*i*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^4*(c*i + d*i*x)), x, 11, (-6*b*B^2*d^2*n^2*(c + d*x))/((b*c - a*d)^4*g^4*i*(a + b*x)) + (3*b^2*B^2*d*n^2*(c + d*x)^2)/(4*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (2*b^3*B^2*n^2*(c + d*x)^3)/(27*(b*c - a*d)^4*g^4*i*(a + b*x)^3) - (6*b*B*d^2*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^4*g^4*i*(a + b*x)) + (3*b^2*B*d*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (2*b^3*B*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(9*(b*c - a*d)^4*g^4*i*(a + b*x)^3) - (3*b*d^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^4*g^4*i*(a + b*x)) + (3*b^2*d*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^4*g^4*i*(a + b*x)^2) - (b^3*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*(b*c - a*d)^4*g^4*i*(a + b*x)^3) - (d^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(3*B*(b*c - a*d)^4*g^4*i*n)]


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x)^2, x, 18, (2*A*B*(b*c - a*d)^2*g^3*n*(a + b*x))/(d^3*i^2*(c + d*x)) - (2*B^2*(b*c - a*d)^2*g^3*n^2*(a + b*x))/(d^3*i^2*(c + d*x)) + (2*B^2*(b*c - a*d)^2*g^3*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d^3*i^2*(c + d*x)) - (b*B*(b*c - a*d)*g^3*n*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(d^3*i^2) - (3*b*(b*c - a*d)*g^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d^3*i^2) - ((b*c - a*d)^2*g^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d^3*i^2*(c + d*x)) + (b^3*g^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*d^4*i^2) - (6*b*B*(b*c - a*d)^2*g^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^4*i^2) - (3*b*(b*c - a*d)^2*g^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log((b*c - a*d)/(b*(c + d*x))))/(d^4*i^2) + (b*B^2*(b*c - a*d)^2*g^3*n^2*log(c + d*x))/(d^4*i^2) + (b*B*(b*c - a*d)^2*g^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log(1 - (b*(c + d*x))/(d*(a + b*x))))/(d^4*i^2) - (6*b*B^2*(b*c - a*d)^2*g^3*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^2) - (6*b*B*(b*c - a*d)^2*g^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^2) - (b*B^2*(b*c - a*d)^2*g^3*n^2*PolyLog(2, (b*(c + d*x))/(d*(a + b*x))))/(d^4*i^2) + (6*b*B^2*(b*c - a*d)^2*g^3*n^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^2)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x)^2, x, 12, (-2*A*B*(b*c - a*d)*g^2*n*(a + b*x))/(d^2*i^2*(c + d*x)) + (2*B^2*(b*c - a*d)*g^2*n^2*(a + b*x))/(d^2*i^2*(c + d*x)) - (2*B^2*(b*c - a*d)*g^2*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d^2*i^2*(c + d*x)) + (b*g^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d^2*i^2) + ((b*c - a*d)*g^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d^2*i^2*(c + d*x)) + (2*b*B*(b*c - a*d)*g^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^3*i^2) + (2*b*(b*c - a*d)*g^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log((b*c - a*d)/(b*(c + d*x))))/(d^3*i^2) + (2*b*B^2*(b*c - a*d)*g^2*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^2) + (4*b*B*(b*c - a*d)*g^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^2) - (4*b*B^2*(b*c - a*d)*g^2*n^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^2)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x)^2, x, 9, (2*A*B*g*n*(a + b*x))/(d*i^2*(c + d*x)) - (2*B^2*g*n^2*(a + b*x))/(d*i^2*(c + d*x)) + (2*B^2*g*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d*i^2*(c + d*x)) - (g*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d*i^2*(c + d*x)) - (b*g*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log((b*c - a*d)/(b*(c + d*x))))/(d^2*i^2) - (2*b*B*g*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i^2) + (2*b*B^2*g*n^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^2*i^2)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x)^2, x, 4, (-2*A*B*n*(a + b*x))/((b*c - a*d)*i^2*(c + d*x)) + (2*B^2*n^2*(a + b*x))/((b*c - a*d)*i^2*(c + d*x)) - (2*B^2*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)*i^2*(c + d*x)) + ((a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)*i^2*(c + d*x))]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^1*(c*i + d*i*x)^2), x, 7, (2*A*B*d*n*(a + b*x))/((b*c - a*d)^2*g*i^2*(c + d*x)) - (2*B^2*d*n^2*(a + b*x))/((b*c - a*d)^2*g*i^2*(c + d*x)) + (2*B^2*d*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^2*g*i^2*(c + d*x)) - (d*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^2*g*i^2*(c + d*x)) + (b*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(3*B*(b*c - a*d)^2*g*i^2*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^2*(c*i + d*i*x)^2), x, 10, (-2*A*B*d^2*n*(a + b*x))/((b*c - a*d)^3*g^2*i^2*(c + d*x)) + (2*B^2*d^2*n^2*(a + b*x))/((b*c - a*d)^3*g^2*i^2*(c + d*x)) - (2*b^2*B^2*n^2*(c + d*x))/((b*c - a*d)^3*g^2*i^2*(a + b*x)) - (2*B^2*d^2*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^3*g^2*i^2*(c + d*x)) - (2*b^2*B*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^3*g^2*i^2*(a + b*x)) + (d^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^3*g^2*i^2*(c + d*x)) - (b^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^3*g^2*i^2*(a + b*x)) - (2*b*d*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(3*B*(b*c - a*d)^3*g^2*i^2*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^3*(c*i + d*i*x)^2), x, 12, (2*A*B*d^3*n*(a + b*x))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) - (2*B^2*d^3*n^2*(a + b*x))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (6*b^2*B^2*d*n^2*(c + d*x))/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*B^2*n^2*(c + d*x)^2)/(4*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) + (2*B^2*d^3*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (6*b^2*B*d*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*B*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) - (d^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^4*g^3*i^2*(c + d*x)) + (3*b^2*d*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^4*g^3*i^2*(a + b*x)) - (b^3*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^4*g^3*i^2*(a + b*x)^2) + (b*d^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(B*(b*c - a*d)^4*g^3*i^2*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^4*(c*i + d*i*x)^2), x, 14, (-2*A*B*d^4*n*(a + b*x))/((b*c - a*d)^5*g^4*i^2*(c + d*x)) + (2*B^2*d^4*n^2*(a + b*x))/((b*c - a*d)^5*g^4*i^2*(c + d*x)) - (12*b^2*B^2*d^2*n^2*(c + d*x))/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (b^3*B^2*d*n^2*(c + d*x)^2)/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (2*b^4*B^2*n^2*(c + d*x)^3)/(27*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) - (2*B^2*d^4*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^5*g^4*i^2*(c + d*x)) - (12*b^2*B*d^2*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (2*b^3*B*d*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (2*b^4*B*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(9*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) + (d^4*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^5*g^4*i^2*(c + d*x)) - (6*b^2*d^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^5*g^4*i^2*(a + b*x)) + (2*b^3*d*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^5*g^4*i^2*(a + b*x)^2) - (b^4*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*(b*c - a*d)^5*g^4*i^2*(a + b*x)^3) - (4*b*d^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(3*B*(b*c - a*d)^5*g^4*i^2*n)]


    @test_int [(a*g + b*g*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x)^3, x, 14, (B^2*(b*c - a*d)*g^3*n^2*(a + b*x)^2)/(4*d^2*i^3*(c + d*x)^2) - (4*A*b*B*(b*c - a*d)*g^3*n*(a + b*x))/(d^3*i^3*(c + d*x)) + (4*b*B^2*(b*c - a*d)*g^3*n^2*(a + b*x))/(d^3*i^3*(c + d*x)) - (4*b*B^2*(b*c - a*d)*g^3*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d^3*i^3*(c + d*x)) - (B*(b*c - a*d)*g^3*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d^2*i^3*(c + d*x)^2) + (b^2*g^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d^3*i^3) + ((b*c - a*d)*g^3*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*d^2*i^3*(c + d*x)^2) + (2*b*(b*c - a*d)*g^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d^3*i^3*(c + d*x)) + (2*b^2*B*(b*c - a*d)*g^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*log((b*c - a*d)/(b*(c + d*x))))/(d^4*i^3) + (3*b^2*(b*c - a*d)*g^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log((b*c - a*d)/(b*(c + d*x))))/(d^4*i^3) + (2*b^2*B^2*(b*c - a*d)*g^3*n^2*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^3) + (6*b^2*B*(b*c - a*d)*g^3*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^3) - (6*b^2*B^2*(b*c - a*d)*g^3*n^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^4*i^3)]
    @test_int [(a*g + b*g*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x)^3, x, 11, -(B^2*g^2*n^2*(a + b*x)^2)/(4*d*i^3*(c + d*x)^2) + (2*A*b*B*g^2*n*(a + b*x))/(d^2*i^3*(c + d*x)) - (2*b*B^2*g^2*n^2*(a + b*x))/(d^2*i^3*(c + d*x)) + (2*b*B^2*g^2*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/(d^2*i^3*(c + d*x)) + (B*g^2*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*d*i^3*(c + d*x)^2) - (g^2*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*d*i^3*(c + d*x)^2) - (b*g^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(d^2*i^3*(c + d*x)) - (b^2*g^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2*log((b*c - a*d)/(b*(c + d*x))))/(d^3*i^3) - (2*b^2*B*g^2*n*(A + B*log(e*((a + b*x)/(c + d*x))^n))*PolyLog(2, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^3) + (2*b^2*B^2*g^2*n^2*PolyLog(3, (d*(a + b*x))/(b*(c + d*x))))/(d^3*i^3)]
    @test_int [(a*g + b*g*x)^1*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x)^3, x, 3, (B^2*g*n^2*(a + b*x)^2)/(4*(b*c - a*d)*i^3*(c + d*x)^2) - (B*g*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)*i^3*(c + d*x)^2) + (g*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)*i^3*(c + d*x)^2)]
    @test_int [(a*g + b*g*x)^0*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x)^3, x, 8, -(B^2*d*n^2*(a + b*x)^2)/(4*(b*c - a*d)^2*i^3*(c + d*x)^2) - (2*A*b*B*n*(a + b*x))/((b*c - a*d)^2*i^3*(c + d*x)) + (2*b*B^2*n^2*(a + b*x))/((b*c - a*d)^2*i^3*(c + d*x)) - (2*b*B^2*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^2*i^3*(c + d*x)) + (B*d*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^2*i^3*(c + d*x)^2) - (d*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^2*i^3*(c + d*x)^2) + (b*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^2*i^3*(c + d*x))]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^1*(c*i + d*i*x)^3), x, 15, (B^2*d^2*n^2*(a + b*x)^2)/(4*(b*c - a*d)^3*g*i^3*(c + d*x)^2) + (4*A*b*B*d*n*(a + b*x))/((b*c - a*d)^3*g*i^3*(c + d*x)) - (4*b*B^2*d*n^2*(a + b*x))/((b*c - a*d)^3*g*i^3*(c + d*x)) + (4*b*B^2*d*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^3*g*i^3*(c + d*x)) - (B*d^2*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^3*g*i^3*(c + d*x)^2) + (d^2*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^3*g*i^3*(c + d*x)^2) - (2*b*d*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^3*g*i^3*(c + d*x)) + (b^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(3*B*(b*c - a*d)^3*g*i^3*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^2*(c*i + d*i*x)^3), x, 12, -(B^2*d^3*n^2*(a + b*x)^2)/(4*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2) - (6*A*b*B*d^2*n*(a + b*x))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) + (6*b*B^2*d^2*n^2*(a + b*x))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) - (2*b^3*B^2*n^2*(c + d*x))/((b*c - a*d)^4*g^2*i^3*(a + b*x)) - (6*b*B^2*d^2*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^4*g^2*i^3*(c + d*x)) + (B*d^3*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2) - (2*b^3*B*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^4*g^2*i^3*(a + b*x)) - (d^3*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^4*g^2*i^3*(c + d*x)^2) + (3*b*d^2*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^4*g^2*i^3*(c + d*x)) - (b^3*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^4*g^2*i^3*(a + b*x)) - (b^2*d*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(B*(b*c - a*d)^4*g^2*i^3*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^3*(c*i + d*i*x)^3), x, 14, (B^2*d^4*n^2*(a + b*x)^2)/(4*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2) + (8*A*b*B*d^3*n*(a + b*x))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) - (8*b*B^2*d^3*n^2*(a + b*x))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) + (8*b^3*B^2*d*n^2*(c + d*x))/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*B^2*n^2*(c + d*x)^2)/(4*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) + (8*b*B^2*d^3*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^5*g^3*i^3*(c + d*x)) - (B*d^4*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2) + (8*b^3*B*d*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*B*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) + (d^4*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^5*g^3*i^3*(c + d*x)^2) - (4*b*d^3*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^5*g^3*i^3*(c + d*x)) + (4*b^3*d*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^5*g^3*i^3*(a + b*x)) - (b^4*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^5*g^3*i^3*(a + b*x)^2) + (2*b^2*d^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(B*(b*c - a*d)^5*g^3*i^3*n)]
    @test_int [(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/((a*g + b*g*x)^4*(c*i + d*i*x)^3), x, 16, -(B^2*d^5*n^2*(a + b*x)^2)/(4*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2) - (10*A*b*B*d^4*n*(a + b*x))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) + (10*b*B^2*d^4*n^2*(a + b*x))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) - (20*b^3*B^2*d^2*n^2*(c + d*x))/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*B^2*d*n^2*(c + d*x)^2)/(4*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (2*b^5*B^2*n^2*(c + d*x)^3)/(27*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) - (10*b*B^2*d^4*n*(a + b*x)*log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)^6*g^4*i^3*(c + d*x)) + (B*d^5*n*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2) - (20*b^3*B*d^2*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*B*d*n*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(2*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (2*b^5*B*n*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(9*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) - (d^5*(a + b*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^6*g^4*i^3*(c + d*x)^2) + (5*b*d^4*(a + b*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^6*g^4*i^3*(c + d*x)) - (10*b^3*d^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)^6*g^4*i^3*(a + b*x)) + (5*b^4*d*(c + d*x)^2*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(2*(b*c - a*d)^6*g^4*i^3*(a + b*x)^2) - (b^5*(c + d*x)^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/(3*(b*c - a*d)^6*g^4*i^3*(a + b*x)^3) - (10*b^2*d^3*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/(3*B*(b*c - a*d)^6*g^4*i^3*n)]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*((a+b*x) / (c+d*x))^n))^p*when*b*f-a*g=0*and*d*h-c*i=0*and*m+q+2=0=#


    @test_int [(a*g + b*g*x)^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^p/(c*i + d*i*x)^(m + 2), x, 3, ((a + b*x)*(g*(a + b*x))^m*Gamma(1 + p, -(((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n)))*(A + B*log(e*((a + b*x)/(c + d*x))^n))^p)/(ℯ^((A*(1 + m))/(B*n))*(e*((a + b*x)/(c + d*x))^n)^((1 + m)/n)*(i*(c + d*x))^m*(-(((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n)))^p*((b*c - a*d)*i^2*(1 + m)*(c + d*x)))]
    @test_int [(c*i + d*i*x)^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^p/(a*g + b*g*x)^(m + 2), x, 3, -((ℯ^((A*(1 + m))/(B*n))*(a + b*x)*(g*(a + b*x))^(-2 - m)*(e*((a + b*x)/(c + d*x))^n)^((1 + m)/n)*(i*(c + d*x))^(2 + m)*Gamma(1 + p, ((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n))*(A + B*log(e*((a + b*x)/(c + d*x))^n))^p)/((((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n))^p*((b*c - a*d)*i^2*(1 + m)*(c + d*x))))]


    @test_int [(a*g + b*g*x)^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3/(c*i + d*i*x)^(m + 2), x, 4, -((6*B^3*n^3*(a + b*x)*(g*(a + b*x))^m)/((i*(c + d*x))^m*((b*c - a*d)*i^2*(1 + m)^4*(c + d*x)))) + (6*B^2*n^2*(a + b*x)*(g*(a + b*x))^m*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((i*(c + d*x))^m*((b*c - a*d)*i^2*(1 + m)^3*(c + d*x))) - (3*B*n*(a + b*x)*(g*(a + b*x))^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((i*(c + d*x))^m*((b*c - a*d)*i^2*(1 + m)^2*(c + d*x))) + ((a + b*x)*(g*(a + b*x))^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/((i*(c + d*x))^m*((b*c - a*d)*i^2*(1 + m)*(c + d*x)))]
    @test_int [(a*g + b*g*x)^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(c*i + d*i*x)^(m + 2), x, 3, (2*B^2*n^2*(a + b*x)*(g*(a + b*x))^m)/((i*(c + d*x))^m*((b*c - a*d)*i^2*(1 + m)^3*(c + d*x))) - (2*B*n*(a + b*x)*(g*(a + b*x))^m*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((i*(c + d*x))^m*((b*c - a*d)*i^2*(1 + m)^2*(c + d*x))) + ((a + b*x)*(g*(a + b*x))^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((i*(c + d*x))^m*((b*c - a*d)*i^2*(1 + m)*(c + d*x)))]
    @test_int [(a*g + b*g*x)^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^1/(c*i + d*i*x)^(m + 2), x, 2, -((B*n*(a + b*x)*(g*(a + b*x))^m)/((i*(c + d*x))^m*((b*c - a*d)*i^2*(1 + m)^2*(c + d*x)))) + ((a + b*x)*(g*(a + b*x))^m*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((i*(c + d*x))^m*((b*c - a*d)*i^2*(1 + m)*(c + d*x)))]
    @test_int [(a*g + b*g*x)^m/((c*i + d*i*x)^(m + 2)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^1), x, 3, ((a + b*x)*(g*(a + b*x))^m*ExpIntegralEi(((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n)))/(ℯ^((A*(1 + m))/(B*n))*(e*((a + b*x)/(c + d*x))^n)^((1 + m)/n)*(i*(c + d*x))^m*(B*(b*c - a*d)*i^2*n*(c + d*x)))]
    @test_int [(a*g + b*g*x)^m/((c*i + d*i*x)^(m + 2)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2), x, 4, ((1 + m)*(a + b*x)*(g*(a + b*x))^m*ExpIntegralEi(((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n)))/(ℯ^((A*(1 + m))/(B*n))*(e*((a + b*x)/(c + d*x))^n)^((1 + m)/n)*(i*(c + d*x))^m*(B^2*(b*c - a*d)*i^2*n^2*(c + d*x))) - ((a + b*x)*(g*(a + b*x))^m)/((i*(c + d*x))^m*(B*(b*c - a*d)*i^2*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))))]
    @test_int [(a*g + b*g*x)^m/((c*i + d*i*x)^(m + 2)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3), x, 5, ((1 + m)^2*(a + b*x)*(g*(a + b*x))^m*ExpIntegralEi(((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n)))/(ℯ^((A*(1 + m))/(B*n))*(e*((a + b*x)/(c + d*x))^n)^((1 + m)/n)*(i*(c + d*x))^m*(2*B^3*(b*c - a*d)*i^2*n^3*(c + d*x))) - ((a + b*x)*(g*(a + b*x))^m)/((i*(c + d*x))^m*(2*B*(b*c - a*d)*i^2*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)) - ((1 + m)*(a + b*x)*(g*(a + b*x))^m)/((i*(c + d*x))^m*(2*B^2*(b*c - a*d)*i^2*n^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))))]


    @test_int [(c*i + d*i*x)^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3/(a*g + b*g*x)^(m + 2), x, 4, -((6*B^3*n^3*(a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m))/((b*c - a*d)*i^2*(1 + m)^4*(c + d*x))) - (6*B^2*n^2*(a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)*i^2*(1 + m)^3*(c + d*x)) - (3*B*n*(a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)*i^2*(1 + m)^2*(c + d*x)) - ((a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3)/((b*c - a*d)*i^2*(1 + m)*(c + d*x))]
    @test_int [(c*i + d*i*x)^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2/(a*g + b*g*x)^(m + 2), x, 3, -((2*B^2*n^2*(a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m))/((b*c - a*d)*i^2*(1 + m)^3*(c + d*x))) - (2*B*n*(a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)*i^2*(1 + m)^2*(c + d*x)) - ((a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2)/((b*c - a*d)*i^2*(1 + m)*(c + d*x))]
    @test_int [(c*i + d*i*x)^m*(A + B*log(e*((a + b*x)/(c + d*x))^n))^1/(a*g + b*g*x)^(m + 2), x, 2, -((B*n*(a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m))/((b*c - a*d)*i^2*(1 + m)^2*(c + d*x))) - ((a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/((b*c - a*d)*i^2*(1 + m)*(c + d*x))]
    @test_int [(c*i + d*i*x)^m/((a*g + b*g*x)^(m + 2)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^1), x, 3, (ℯ^((A*(1 + m))/(B*n))*(a + b*x)*(g*(a + b*x))^(-2 - m)*(e*((a + b*x)/(c + d*x))^n)^((1 + m)/n)*(i*(c + d*x))^(2 + m)*ExpIntegralEi(-(((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n))))/(B*(b*c - a*d)*i^2*n*(c + d*x))]
    @test_int [(c*i + d*i*x)^m/((a*g + b*g*x)^(m + 2)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2), x, 4, -((ℯ^((A*(1 + m))/(B*n))*(1 + m)*(a + b*x)*(g*(a + b*x))^(-2 - m)*(e*((a + b*x)/(c + d*x))^n)^((1 + m)/n)*(i*(c + d*x))^(2 + m)*ExpIntegralEi(-(((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n))))/(B^2*(b*c - a*d)*i^2*n^2*(c + d*x))) - ((a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m))/(B*(b*c - a*d)*i^2*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))]
    @test_int [(c*i + d*i*x)^m/((a*g + b*g*x)^(m + 2)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^3), x, 5, (ℯ^((A*(1 + m))/(B*n))*(1 + m)^2*(a + b*x)*(g*(a + b*x))^(-2 - m)*(e*((a + b*x)/(c + d*x))^n)^((1 + m)/n)*(i*(c + d*x))^(2 + m)*ExpIntegralEi(-(((1 + m)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))/(B*n))))/(2*B^3*(b*c - a*d)*i^2*n^3*(c + d*x)) - ((a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m))/(2*B*(b*c - a*d)*i^2*n*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2) + ((1 + m)*(a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m))/(2*B^2*(b*c - a*d)*i^2*n^2*(c + d*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n)))]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*((a+b*x) / (c+d*x))^n))^p*when*b*f-a*g=0*and*d*h-c*i=0*and*p*symbolic=#


    @test_int [log(e*((a + b*x)/(c + d*x))^n)^p/((a + b*x)*(c + d*x)), x, 3, log(e*((a + b*x)/(c + d*x))^n)^(1 + p)/((b*c - a*d)*n*(1 + p))]
    @test_int [log(e*((a + b*x)/(c + d*x))^n)^p/(a*c + (b*c + a*d)*x + b*d*x^2), x, 4, log(e*((a + b*x)/(c + d*x))^n)^(1 + p)/((b*c - a*d)*n*(1 + p))]


    #= ::Section:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*((a+b*x)/(c+d*x))^n))^p*when*b*f-a*g=0=#


    #= ::Section:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*((a+b*x)/(c+d*x))^n))^p=#


    #= ::Title:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p=#


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p*when*b*f-a*g=0*and*d*h-c*i=0=#


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))*when*b*f-a*g=0*and*d*h-c*i=0=#


    @test_int [(a*g + b*g*x)^m*(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^p/(c*i + d*i*x)^(m + 2), x, 4, ((a + b*x)*(g*(a + b*x))^m*Gamma(1 + p, -(((1 + m)*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n)))/(B*n)))*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^p)/(ℯ^((A*(1 + m))/(B*n))*((e*(a + b*x)^n)/(c + d*x)^n)^((1 + m)/n)*(i*(c + d*x))^m*(-(((1 + m)*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n)))/(B*n)))^p*((b*c - a*d)*i^2*(1 + m)*(c + d*x)))]
    @test_int [(c*i + d*i*x)^m*(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^p/(a*g + b*g*x)^(m + 2), x, 4, -((1/((b*c - a*d)*i^2*(1 + m)*(c + d*x)))*((ℯ^((A*(1 + m))/(B*n))*(a + b*x)*(g*(a + b*x))^(-2 - m)*(i*(c + d*x))^(2 + m)*((e*(a + b*x)^n)/(c + d*x)^n)^((1 + m)/n)*Gamma(1 + p, ((1 + m)*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n)))/(B*n))*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^p)/(((1 + m)*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n)))/(B*n))^p))]


    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^3/((a + b*x)*(c + d*x)), x, 4, (A + B*log(e*(a + b*x)^n/(c + d*x)^n))^4/(4*B*(b*c - a*d)*n)]
    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^2/((a + b*x)*(c + d*x)), x, 4, (A + B*log(e*(a + b*x)^n/(c + d*x)^n))^3/(3*B*(b*c - a*d)*n)]
    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^1/((a + b*x)*(c + d*x)), x, 3, (A + B*log(e*(a + b*x)^n/(c + d*x)^n))^2/(2*B*(b*c - a*d)*n)]
    @test_int [1/((A + B*log(e*(a + b*x)^n/(c + d*x)^n))^1*(a + b*x)*(c + d*x)), x, 4, log(A + B*log(e*(a + b*x)^n/(c + d*x)^n))/(B*(b*c - a*d)*n)]
    @test_int [1/((A + B*log(e*(a + b*x)^n/(c + d*x)^n))^2*(a + b*x)*(c + d*x)), x, 4, -(1/(B*(b*c - a*d)*n*(A + B*log(e*(a + b*x)^n/(c + d*x)^n))))]
    @test_int [1/((A + B*log(e*(a + b*x)^n/(c + d*x)^n))^3*(a + b*x)*(c + d*x)), x, 4, -(1/(2*B*(b*c - a*d)*n*(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^2))]


    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^p/((a + b*x)*(c + d*x)), x, 4, (A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^(1 + p)/(B*(b*c - a*d)*n*(1 + p))]
    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^p/((a*f + b*f*x)*(c*g + d*g*x)), x, 4, (A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^(1 + p)/(B*(b*c - a*d)*f*g*n*(1 + p))]
    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^p/(a*c*f + (b*c + a*d)*f*x + b*d*f*x^2), x, 5, (A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^(1 + p)/(B*(b*c - a*d)*f*n*(1 + p))]


    @test_int [1/(A + B*log(e*(a + b*x)^n/(c + d*x)^n))/((a + b*x)*(c + d*x)), x, 4, log(A + B*log(e*(a + b*x)^n/(c + d*x)^n))/(B*(b*c - a*d)*n)]
    @test_int [1/(A + B*log(e*(a + b*x)^n/(c + d*x)^n))/((a*f + b*f*x)*(c*g + d*g*x)), x, 4, log(A + B*log(e*(a + b*x)^n/(c + d*x)^n))/(B*(b*c - a*d)*f*g*n)]
    @test_int [1/(A + B*log(e*(a + b*x)^n/(c + d*x)^n))/(a*c*f + (b*c + a*d)*f*x + b*d*f*x^2), x, 5, log(A + B*log(e*(a + b*x)^n/(c + d*x)^n))/(B*(b*c - a*d)*f*n)]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q / (A+B*log(e*(a+b*x)^n/(c+d*x)^n))*when*b*f-a*g=0*and*d*h-c*i=0*and*m+n+2=0=#


    @test_int [(a + b*x)^m/((c + d*x)^(m + 2)*log(e*(a + b*x)^n/(c + d*x)^n)), x, 4, ((a + b*x)^(1 + m)*(c + d*x)^(-1 - m)*ExpIntegralEi(((1 + m)*log((e*(a + b*x)^n)/(c + d*x)^n))/n))/(((e*(a + b*x)^n)/(c + d*x)^n)^((1 + m)/n)*((b*c - a*d)*n))]


    @test_int [(a + b*x)^3/((c + d*x)^5*log(e*((a + b*x)/(c + d*x))^n)), x, 3, ((a + b*x)^4*ExpIntegralEi((4*log(e*((a + b*x)/(c + d*x))^n))/n))/((e*((a + b*x)/(c + d*x))^n)^(4/n)*((b*c - a*d)*n*(c + d*x)^4))]
    @test_int [(a + b*x)^2/((c + d*x)^4*log(e*((a + b*x)/(c + d*x))^n)), x, 3, ((a + b*x)^3*ExpIntegralEi((3*log(e*((a + b*x)/(c + d*x))^n))/n))/((e*((a + b*x)/(c + d*x))^n)^(3/n)*((b*c - a*d)*n*(c + d*x)^3))]
    @test_int [(a + b*x)^1/((c + d*x)^3*log(e*((a + b*x)/(c + d*x))^n)), x, 3, ((a + b*x)^2*ExpIntegralEi((2*log(e*((a + b*x)/(c + d*x))^n))/n))/((e*((a + b*x)/(c + d*x))^n)^(2/n)*((b*c - a*d)*n*(c + d*x)^2))]
    @test_int [(a + b*x)^0/((c + d*x)^2*log(e*((a + b*x)/(c + d*x))^n)), x, 3, ((a + b*x)*ExpIntegralEi(log(e*((a + b*x)/(c + d*x))^n)/n))/((e*((a + b*x)/(c + d*x))^n)^n^(-1)*((b*c - a*d)*n*(c + d*x)))]
    @test_int [1/((a + b*x)^1*(c + d*x)^1*log(e*((a + b*x)/(c + d*x))^n)), x, 3, log(log(e*((a + b*x)/(c + d*x))^n))/((b*c - a*d)*n)]
    @test_int [1/((a + b*x)^2*(c + d*x)^0*log(e*((a + b*x)/(c + d*x))^n)), x, 3, ((e*((a + b*x)/(c + d*x))^n)^(1/n)*(c + d*x)*ExpIntegralEi(-(log(e*((a + b*x)/(c + d*x))^n)/n)))/((b*c - a*d)*n*(a + b*x))]
    @test_int [1/((a + b*x)^3*(c + d*x)^(-1)*log(e*((a + b*x)/(c + d*x))^n)), x, 3, ((e*((a + b*x)/(c + d*x))^n)^(2/n)*(c + d*x)^2*ExpIntegralEi(-((2*log(e*((a + b*x)/(c + d*x))^n))/n)))/((b*c - a*d)*n*(a + b*x)^2)]
    @test_int [1/((a + b*x)^4*(c + d*x)^(-2)*log(e*((a + b*x)/(c + d*x))^n)), x, 3, ((e*((a + b*x)/(c + d*x))^n)^(3/n)*(c + d*x)^3*ExpIntegralEi(-((3*log(e*((a + b*x)/(c + d*x))^n))/n)))/((b*c - a*d)*n*(a + b*x)^3)]


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f+g*x)^m*(h+i*x)^q*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p*when*b*f-a*g=0=#


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p / ((f+g*x)*(h+i*x))*when*b*f-a*g=0=#


    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^4/((a*h + b*h*x)*(f + g*x)), x, 8, -(((A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^4*log(1 - ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)) + (4*B*n*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^3*PolyLog(2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h) + (12*B^2*n^2*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^2*PolyLog(3, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h) + (24*B^3*n^3*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))*PolyLog(4, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h) + (24*B^4*n^4*PolyLog(5, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)]
    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^3/((a*h + b*h*x)*(f + g*x)), x, 7, -(((A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^3*log(1 - ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)) + (3*B*n*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^2*PolyLog(2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h) + (6*B^2*n^2*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))*PolyLog(3, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h) + (6*B^3*n^3*PolyLog(4, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)]
    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^2/((a*h + b*h*x)*(f + g*x)), x, 6, -(((A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^2*log(1 - ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)) + (2*B*n*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))*PolyLog(2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h) + (2*B^2*n^2*PolyLog(3, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)]
    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^1/((a*h + b*h*x)*(f + g*x)), x, 5, -(((A + B*log((e*(a + b*x)^n)/(c + d*x)^n))*log(1 - ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)) + (B*n*PolyLog(2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)]
    @test_int [1/((A + B*log(e*(a + b*x)^n/(c + d*x)^n))^1*(a*h + b*h*x)*(f + g*x)), x, 1, Defer(Subst)(Unintegrable(1/((f + g*x)*(a*h + b*h*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))), x), e*((a + b*x)/(c + d*x))^n, (e*(a + b*x)^n)/(c + d*x)^n)]
    @test_int [1/((A + B*log(e*(a + b*x)^n/(c + d*x)^n))^2*(a*h + b*h*x)*(f + g*x)), x, 1, Defer(Subst)(Unintegrable(1/((f + g*x)*(a*h + b*h*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2), x), e*((a + b*x)/(c + d*x))^n, (e*(a + b*x)^n)/(c + d*x)^n)]


    @test_int [log((c + d*x)/(a + b*x))/((a + b*x)*(h*(a - c) + h*(b - d)*x)), x, 2, -(PolyLog(2, 1 - (c + d*x)/(a + b*x))/((b*c - a*d)*h))]


    @test_int [log((a - c*g + (b - d*g)*x)/(a + b*x))/((a + b*x)*(c + d*x)), x, 2, PolyLog(2, (g*(c + d*x))/(a + b*x))/(b*c - a*d)]
    @test_int [log(1 - (g*(c + d*x))/(a + b*x))/((a + b*x)*(c + d*x)), x, 3, PolyLog(2, (g*(c + d*x))/(a + b*x))/(b*c - a*d)]
    @test_int [log((a - c*g + b*x - d*g*x)/(a + b*x))/((a + b*x)*(c + d*x)), x, 3, PolyLog(2, (g*(c + d*x))/(a + b*x))/(b*c - a*d)]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(A+B*log(e*(a+b*x)^n/(c+d*x)^n))^p / (g+h*x+i*x^2)=#


    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^3/(a*f*h + h*(b*f*x + a*g*x) + b*g*h*x^2), x, 8, -(((A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^3*log(1 - ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)) + (3*B*n*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^2*PolyLog(2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h) + (6*B^2*n^2*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))*PolyLog(3, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h) + (6*B^3*n^3*PolyLog(4, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)]
    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^2/(a*f*h + h*(b*f*x + a*g*x) + b*g*h*x^2), x, 7, -(((A + B*log((e*(a + b*x)^n)/(c + d*x)^n))^2*log(1 - ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)) + (2*B*n*(A + B*log((e*(a + b*x)^n)/(c + d*x)^n))*PolyLog(2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h) + (2*B^2*n^2*PolyLog(3, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)]
    @test_int [(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^1/(a*f*h + h*(b*f*x + a*g*x) + b*g*h*x^2), x, 6, -(((A + B*log((e*(a + b*x)^n)/(c + d*x)^n))*log(1 - ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)) + (B*n*PolyLog(2, ((b*f - a*g)*(c + d*x))/((d*f - c*g)*(a + b*x))))/((b*f - a*g)*h)]
    @test_int [1/(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^1/(a*f*h + h*(b*f*x + a*g*x) + b*g*h*x^2), x, 3, Defer(Subst)(Unintegrable(1/((a + b*x)*(f + g*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))), x), e*((a + b*x)/(c + d*x))^n, (e*(a + b*x)^n)/(c + d*x)^n)/h]
    @test_int [1/(A + B*log(e*(a + b*x)^n/(c + d*x)^n))^2/(a*f*h + h*(b*f*x + a*g*x) + b*g*h*x^2), x, 3, Defer(Subst)(Unintegrable(1/((a + b*x)*(f + g*x)*(A + B*log(e*((a + b*x)/(c + d*x))^n))^2), x), e*((a + b*x)/(c + d*x))^n, (e*(a + b*x)^n)/(c + d*x)^n)/h]
    end
