@testset "4.6.11 (e x)^m (a+b csc(c+d x^n))^p" begin
    (a, b, c, d, e, m, n, p, x, ) = @variables a b c d e m n p x

    #= ::Package:: =#

    #= ::Title:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*csc(c+d*x^n))^p=#


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*csc(c+d*x^2))^p=#


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*csc(c+d*x^2))^p=#


    #= ::Subsubsection::Closed:: =#
    #=p>0=#


    @test_int [x^5*(a + b*csc(c + d*x^2)), x, 10, (a*x^6)/6 - (b*x^4*atanh(ℯ^(im*(c + d*x^2))))/d + (im*b*x^2*PolyLog(2, -ℯ^(im*(c + d*x^2))))/d^2 - (im*b*x^2*PolyLog(2, ℯ^(im*(c + d*x^2))))/d^2 - (b*PolyLog(3, -ℯ^(im*(c + d*x^2))))/d^3 + (b*PolyLog(3, ℯ^(im*(c + d*x^2))))/d^3]
    @test_int [x^4*(a + b*csc(c + d*x^2)), x, 2, (a*x^5)/5 + b*Unintegrable(x^4*csc(c + d*x^2), x)]
    @test_int [x^3*(a + b*csc(c + d*x^2)), x, 8, (a*x^4)/4 - (b*x^2*atanh(ℯ^(im*(c + d*x^2))))/d + ((im/2)*b*PolyLog(2, -ℯ^(im*(c + d*x^2))))/d^2 - ((im/2)*b*PolyLog(2, ℯ^(im*(c + d*x^2))))/d^2]
    @test_int [x^2*(a + b*csc(c + d*x^2)), x, 2, (a*x^3)/3 + b*Unintegrable(x^2*csc(c + d*x^2), x)]
    @test_int [x*(a + b*csc(c + d*x^2)), x, 4, (a*x^2)/2 - (b*atanh(cos(c + d*x^2)))/(2*d)]
    @test_int [(a + b*csc(c + d*x^2))/x, x, 2, a*log(x) + b*Unintegrable(csc(c + d*x^2)/x, x)]
    @test_int [(a + b*csc(c + d*x^2))/x^2, x, 2, -(a/x) + b*Unintegrable(csc(c + d*x^2)/x^2, x)]


    @test_int [x^5*(a + b*csc(c + d*x^2))^2, x, 15, ((-im/2)*b^2*x^4)/d + (a^2*x^6)/6 - (2*a*b*x^4*atanh(ℯ^(im*(c + d*x^2))))/d - (b^2*x^4*cot(c + d*x^2))/(2*d) + (b^2*x^2*log(1 - ℯ^((2*im)*(c + d*x^2))))/d^2 + ((2*im)*a*b*x^2*PolyLog(2, -ℯ^(im*(c + d*x^2))))/d^2 - ((2*im)*a*b*x^2*PolyLog(2, ℯ^(im*(c + d*x^2))))/d^2 - ((im/2)*b^2*PolyLog(2, ℯ^((2*im)*(c + d*x^2))))/d^3 - (2*a*b*PolyLog(3, -ℯ^(im*(c + d*x^2))))/d^3 + (2*a*b*PolyLog(3, ℯ^(im*(c + d*x^2))))/d^3]
    @test_int [x^4*(a + b*csc(c + d*x^2))^2, x, 0, Unintegrable(x^4*(a + b*csc(c + d*x^2))^2, x)]
    @test_int [x^3*(a + b*csc(c + d*x^2))^2, x, 10, (a^2*x^4)/4 - (2*a*b*x^2*atanh(ℯ^(im*(c + d*x^2))))/d - (b^2*x^2*cot(c + d*x^2))/(2*d) + (b^2*log(sin(c + d*x^2)))/(2*d^2) + (im*a*b*PolyLog(2, -ℯ^(im*(c + d*x^2))))/d^2 - (im*a*b*PolyLog(2, ℯ^(im*(c + d*x^2))))/d^2]
    @test_int [x^2*(a + b*csc(c + d*x^2))^2, x, 0, Unintegrable(x^2*(a + b*csc(c + d*x^2))^2, x)]
    @test_int [x*(a + b*csc(c + d*x^2))^2, x, 5, (a^2*x^2)/2 - (a*b*atanh(cos(c + d*x^2)))/d - (b^2*cot(c + d*x^2))/(2*d)]
    @test_int [(a + b*csc(c + d*x^2))^2/x, x, 0, Unintegrable((a + b*csc(c + d*x^2))^2/x, x)]
    @test_int [(a + b*csc(c + d*x^2))^2/x^2, x, 0, Unintegrable((a + b*csc(c + d*x^2))^2/x^2, x)]


    @test_int [x*csc(a + b*x^2)^7, x, 5, (-5*atanh(cos(a + b*x^2)))/(32*b) - (5*cot(a + b*x^2)*csc(a + b*x^2))/(32*b) - (5*cot(a + b*x^2)*csc(a + b*x^2)^3)/(48*b) - (cot(a + b*x^2)*csc(a + b*x^2)^5)/(12*b)]


    #= ::Subsubsection::Closed:: =#
    #=p<0=#


    @test_int [x^5/(a + b*csc(c + d*x^2)), x, 13, x^6/(6*a) + ((im/2)*b*x^4*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) - ((im/2)*b*x^4*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) + (b*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) - (b*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) + (im*b*PolyLog(3, (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - (im*b*PolyLog(3, (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3)]
    @test_int [x^4/(a + b*csc(c + d*x^2)), x, 0, Unintegrable(x^4/(a + b*csc(c + d*x^2)), x)]
    @test_int [x^3/(a + b*csc(c + d*x^2)), x, 11, x^4/(4*a) + ((im/2)*b*x^2*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) - ((im/2)*b*x^2*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) + (b*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(2*a*sqrt(-a^2 + b^2)*d^2) - (b*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(2*a*sqrt(-a^2 + b^2)*d^2)]
    @test_int [x^2/(a + b*csc(c + d*x^2)), x, 0, Unintegrable(x^2/(a + b*csc(c + d*x^2)), x)]
    @test_int [x/(a + b*csc(c + d*x^2)), x, 5, x^2/(2*a) + (b*atanh((a + b*tan((c + d*x^2)/2))/sqrt(a^2 - b^2)))/(a*sqrt(a^2 - b^2)*d)]
    @test_int [1/(x*(a + b*csc(c + d*x^2))), x, 0, Unintegrable(1/(x*(a + b*csc(c + d*x^2))), x)]
    @test_int [(a + b*csc(c + d*x^2))/x^2, x, 2, -(a/x) + b*Unintegrable(csc(c + d*x^2)/x^2, x)]


    @test_int [x^5/(a + b*csc(c + d*x^2))^2, x, 31, ((-im/2)*b^2*x^4)/(a^2*(a^2 - b^2)*d) + x^6/(6*a^2) + (b^2*x^2*log(1 + (a*ℯ^(im*(c + d*x^2)))/(im*b - sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) + (b^2*x^2*log(1 + (a*ℯ^(im*(c + d*x^2)))/(im*b + sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) - ((im/2)*b^3*x^4*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) + (im*b*x^4*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) + ((im/2)*b^3*x^4*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) - (im*b*x^4*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) - (im*b^2*PolyLog(2, -((a*ℯ^(im*(c + d*x^2)))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - (im*b^2*PolyLog(2, -((a*ℯ^(im*(c + d*x^2)))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - (b^3*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (2*b*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (b^3*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (2*b*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) - (im*b^3*PolyLog(3, (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((2*im)*b*PolyLog(3, (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + (im*b^3*PolyLog(3, (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((2*im)*b*PolyLog(3, (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) - (b^2*x^4*cos(c + d*x^2))/(2*a*(a^2 - b^2)*d*(b + a*sin(c + d*x^2)))]
    @test_int [x^4/(a + b*csc(c + d*x^2))^2, x, 0, Unintegrable(x^4/(a + b*csc(c + d*x^2))^2, x)]
    @test_int [x^3/(a + b*csc(c + d*x^2))^2, x, 22, x^4/(4*a^2) - ((im/2)*b^3*x^2*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) + (im*b*x^2*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) + ((im/2)*b^3*x^2*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) - (im*b*x^2*log(1 - (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) + (b^2*log(b + a*sin(c + d*x^2)))/(2*a^2*(a^2 - b^2)*d^2) - (b^3*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(2*a^2*(-a^2 + b^2)^(3/2)*d^2) + (b*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (b^3*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(2*a^2*(-a^2 + b^2)^(3/2)*d^2) - (b*PolyLog(2, (im*a*ℯ^(im*(c + d*x^2)))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) - (b^2*x^2*cos(c + d*x^2))/(2*a*(a^2 - b^2)*d*(b + a*sin(c + d*x^2)))]
    @test_int [x^2/(a + b*csc(c + d*x^2))^2, x, 0, Unintegrable(x^2/(a + b*csc(c + d*x^2))^2, x)]
    @test_int [x/(a + b*csc(c + d*x^2))^2, x, 7, x^2/(2*a^2) + (b*(2*a^2 - b^2)*atanh((a + b*tan((c + d*x^2)/2))/sqrt(a^2 - b^2)))/(a^2*(a^2 - b^2)^(3/2)*d) - (b^2*cot(c + d*x^2))/(2*a*(a^2 - b^2)*d*(a + b*csc(c + d*x^2)))]
    @test_int [1/(x*(a + b*csc(c + d*x^2))^2), x, 0, Unintegrable(1/(x*(a + b*csc(c + d*x^2))^2), x)]
    @test_int [1/(x^2*(a + b*csc(c + d*x^2))^2), x, 0, Unintegrable(1/(x^2*(a + b*csc(c + d*x^2))^2), x)]
    @test_int [1/(x^3*(a + b*csc(c + d*x^2))^2), x, 0, Unintegrable(1/(x^3*(a + b*csc(c + d*x^2))^2), x)]


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*csc(c+d*x^(1/2)))^p=#


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*csc(c+d*x^(1/2)))^p=#


    #= ::Subsubsection::Closed:: =#
    #=p>0=#


    @test_int [x^3*(a + b*csc(c + d*sqrt(x))), x, 20, (a*x^4)/4 - (4*b*x^(7/2)*atanh(ℯ^(im*(c + d*sqrt(x)))))/d + ((14*im)*b*x^3*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((14*im)*b*x^3*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - (84*b*x^(5/2)*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (84*b*x^(5/2)*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3 - ((420*im)*b*x^2*PolyLog(4, -ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((420*im)*b*x^2*PolyLog(4, ℯ^(im*(c + d*sqrt(x)))))/d^4 + (1680*b*x^(3/2)*PolyLog(5, -ℯ^(im*(c + d*sqrt(x)))))/d^5 - (1680*b*x^(3/2)*PolyLog(5, ℯ^(im*(c + d*sqrt(x)))))/d^5 + ((5040*im)*b*x*PolyLog(6, -ℯ^(im*(c + d*sqrt(x)))))/d^6 - ((5040*im)*b*x*PolyLog(6, ℯ^(im*(c + d*sqrt(x)))))/d^6 - (10080*b*sqrt(x)*PolyLog(7, -ℯ^(im*(c + d*sqrt(x)))))/d^7 + (10080*b*sqrt(x)*PolyLog(7, ℯ^(im*(c + d*sqrt(x)))))/d^7 - ((10080*im)*b*PolyLog(8, -ℯ^(im*(c + d*sqrt(x)))))/d^8 + ((10080*im)*b*PolyLog(8, ℯ^(im*(c + d*sqrt(x)))))/d^8]
    @test_int [x^2*(a + b*csc(c + d*sqrt(x))), x, 16, (a*x^3)/3 - (4*b*x^(5/2)*atanh(ℯ^(im*(c + d*sqrt(x)))))/d + ((10*im)*b*x^2*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((10*im)*b*x^2*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - (40*b*x^(3/2)*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (40*b*x^(3/2)*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3 - ((120*im)*b*x*PolyLog(4, -ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((120*im)*b*x*PolyLog(4, ℯ^(im*(c + d*sqrt(x)))))/d^4 + (240*b*sqrt(x)*PolyLog(5, -ℯ^(im*(c + d*sqrt(x)))))/d^5 - (240*b*sqrt(x)*PolyLog(5, ℯ^(im*(c + d*sqrt(x)))))/d^5 + ((240*im)*b*PolyLog(6, -ℯ^(im*(c + d*sqrt(x)))))/d^6 - ((240*im)*b*PolyLog(6, ℯ^(im*(c + d*sqrt(x)))))/d^6]
    @test_int [x*(a + b*csc(c + d*sqrt(x))), x, 12, (a*x^2)/2 - (4*b*x^(3/2)*atanh(ℯ^(im*(c + d*sqrt(x)))))/d + ((6*im)*b*x*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((6*im)*b*x*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - (12*b*sqrt(x)*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (12*b*sqrt(x)*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3 - ((12*im)*b*PolyLog(4, -ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((12*im)*b*PolyLog(4, ℯ^(im*(c + d*sqrt(x)))))/d^4]
    @test_int [(a + b*csc(c + d*sqrt(x)))/x, x, 2, a*log(x) + b*Unintegrable(csc(c + d*sqrt(x))/x, x)]
    @test_int [(a + b*csc(c + d*sqrt(x)))/x^2, x, 2, -(a/x) + b*Unintegrable(csc(c + d*sqrt(x))/x^2, x)]


    @test_int [x^3*(a + b*csc(c + d*sqrt(x)))^2, x, 30, ((-2*im)*b^2*x^(7/2))/d + (a^2*x^4)/4 - (8*a*b*x^(7/2)*atanh(ℯ^(im*(c + d*sqrt(x)))))/d - (2*b^2*x^(7/2)*cot(c + d*sqrt(x)))/d + (14*b^2*x^3*log(1 - ℯ^((2*im)*(c + d*sqrt(x)))))/d^2 + ((28*im)*a*b*x^3*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((28*im)*a*b*x^3*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((42*im)*b^2*x^(5/2)*PolyLog(2, ℯ^((2*im)*(c + d*sqrt(x)))))/d^3 - (168*a*b*x^(5/2)*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (168*a*b*x^(5/2)*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3 + (105*b^2*x^2*PolyLog(3, ℯ^((2*im)*(c + d*sqrt(x)))))/d^4 - ((840*im)*a*b*x^2*PolyLog(4, -ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((840*im)*a*b*x^2*PolyLog(4, ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((210*im)*b^2*x^(3/2)*PolyLog(4, ℯ^((2*im)*(c + d*sqrt(x)))))/d^5 + (3360*a*b*x^(3/2)*PolyLog(5, -ℯ^(im*(c + d*sqrt(x)))))/d^5 - (3360*a*b*x^(3/2)*PolyLog(5, ℯ^(im*(c + d*sqrt(x)))))/d^5 - (315*b^2*x*PolyLog(5, ℯ^((2*im)*(c + d*sqrt(x)))))/d^6 + ((10080*im)*a*b*x*PolyLog(6, -ℯ^(im*(c + d*sqrt(x)))))/d^6 - ((10080*im)*a*b*x*PolyLog(6, ℯ^(im*(c + d*sqrt(x)))))/d^6 - ((315*im)*b^2*sqrt(x)*PolyLog(6, ℯ^((2*im)*(c + d*sqrt(x)))))/d^7 - (20160*a*b*sqrt(x)*PolyLog(7, -ℯ^(im*(c + d*sqrt(x)))))/d^7 + (20160*a*b*sqrt(x)*PolyLog(7, ℯ^(im*(c + d*sqrt(x)))))/d^7 + (315*b^2*PolyLog(7, ℯ^((2*im)*(c + d*sqrt(x)))))/(2*d^8) - ((20160*im)*a*b*PolyLog(8, -ℯ^(im*(c + d*sqrt(x)))))/d^8 + ((20160*im)*a*b*PolyLog(8, ℯ^(im*(c + d*sqrt(x)))))/d^8]
    @test_int [x^2*(a + b*csc(c + d*sqrt(x)))^2, x, 24, ((-2*im)*b^2*x^(5/2))/d + (a^2*x^3)/3 - (8*a*b*x^(5/2)*atanh(ℯ^(im*(c + d*sqrt(x)))))/d - (2*b^2*x^(5/2)*cot(c + d*sqrt(x)))/d + (10*b^2*x^2*log(1 - ℯ^((2*im)*(c + d*sqrt(x)))))/d^2 + ((20*im)*a*b*x^2*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((20*im)*a*b*x^2*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((20*im)*b^2*x^(3/2)*PolyLog(2, ℯ^((2*im)*(c + d*sqrt(x)))))/d^3 - (80*a*b*x^(3/2)*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (80*a*b*x^(3/2)*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3 + (30*b^2*x*PolyLog(3, ℯ^((2*im)*(c + d*sqrt(x)))))/d^4 - ((240*im)*a*b*x*PolyLog(4, -ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((240*im)*a*b*x*PolyLog(4, ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((30*im)*b^2*sqrt(x)*PolyLog(4, ℯ^((2*im)*(c + d*sqrt(x)))))/d^5 + (480*a*b*sqrt(x)*PolyLog(5, -ℯ^(im*(c + d*sqrt(x)))))/d^5 - (480*a*b*sqrt(x)*PolyLog(5, ℯ^(im*(c + d*sqrt(x)))))/d^5 - (15*b^2*PolyLog(5, ℯ^((2*im)*(c + d*sqrt(x)))))/d^6 + ((480*im)*a*b*PolyLog(6, -ℯ^(im*(c + d*sqrt(x)))))/d^6 - ((480*im)*a*b*PolyLog(6, ℯ^(im*(c + d*sqrt(x)))))/d^6]
    @test_int [x*(a + b*csc(c + d*sqrt(x)))^2, x, 18, ((-2*im)*b^2*x^(3/2))/d + (a^2*x^2)/2 - (8*a*b*x^(3/2)*atanh(ℯ^(im*(c + d*sqrt(x)))))/d - (2*b^2*x^(3/2)*cot(c + d*sqrt(x)))/d + (6*b^2*x*log(1 - ℯ^((2*im)*(c + d*sqrt(x)))))/d^2 + ((12*im)*a*b*x*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((12*im)*a*b*x*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((6*im)*b^2*sqrt(x)*PolyLog(2, ℯ^((2*im)*(c + d*sqrt(x)))))/d^3 - (24*a*b*sqrt(x)*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (24*a*b*sqrt(x)*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3 + (3*b^2*PolyLog(3, ℯ^((2*im)*(c + d*sqrt(x)))))/d^4 - ((24*im)*a*b*PolyLog(4, -ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((24*im)*a*b*PolyLog(4, ℯ^(im*(c + d*sqrt(x)))))/d^4]
    @test_int [(a + b*csc(c + d*sqrt(x)))^2/x, x, 0, Unintegrable((a + b*csc(c + d*sqrt(x)))^2/x, x)]
    @test_int [(a + b*csc(c + d*sqrt(x)))^2/x^2, x, 0, Unintegrable((a + b*csc(c + d*sqrt(x)))^2/x^2, x)]


    #= ::Subsubsection::Closed:: =#
    #=p<0=#


    @test_int [x^3/(a + b*csc(c + d*sqrt(x))), x, 23, x^4/(4*a) + ((2*im)*b*x^(7/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) - ((2*im)*b*x^(7/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) + (14*b*x^3*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) - (14*b*x^3*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) + ((84*im)*b*x^(5/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - ((84*im)*b*x^(5/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - (420*b*x^2*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^4) + (420*b*x^2*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^4) - ((1680*im)*b*x^(3/2)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^5) + ((1680*im)*b*x^(3/2)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^5) + (5040*b*x*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^6) - (5040*b*x*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^6) + ((10080*im)*b*sqrt(x)*PolyLog(7, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^7) - ((10080*im)*b*sqrt(x)*PolyLog(7, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^7) - (10080*b*PolyLog(8, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^8) + (10080*b*PolyLog(8, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^8)]
    @test_int [x^2/(a + b*csc(c + d*sqrt(x))), x, 19, x^3/(3*a) + ((2*im)*b*x^(5/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) - ((2*im)*b*x^(5/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) + (10*b*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) - (10*b*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) + ((40*im)*b*x^(3/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - ((40*im)*b*x^(3/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - (120*b*x*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^4) + (120*b*x*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^4) - ((240*im)*b*sqrt(x)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^5) + ((240*im)*b*sqrt(x)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^5) + (240*b*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^6) - (240*b*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^6)]
    @test_int [x/(a + b*csc(c + d*sqrt(x))), x, 15, x^2/(2*a) + ((2*im)*b*x^(3/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) - ((2*im)*b*x^(3/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) + (6*b*x*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) - (6*b*x*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) + ((12*im)*b*sqrt(x)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - ((12*im)*b*sqrt(x)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - (12*b*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^4) + (12*b*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^4)]
    @test_int [1/(x*(a + b*csc(c + d*sqrt(x)))), x, 0, Unintegrable(1/(x*(a + b*csc(c + d*sqrt(x)))), x)]
    @test_int [(a + b*csc(c + d*sqrt(x)))/x^2, x, 2, -(a/x) + b*Unintegrable(csc(c + d*sqrt(x))/x^2, x)]


    @test_int [x^3/(a + b*csc(c + d*sqrt(x)))^2, x, 61, ((-2*im)*b^2*x^(7/2))/(a^2*(a^2 - b^2)*d) + x^4/(4*a^2) + (14*b^2*x^3*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) + (14*b^2*x^3*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) - ((2*im)*b^3*x^(7/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*im)*b*x^(7/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) + ((2*im)*b^3*x^(7/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*im)*b*x^(7/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) - ((84*im)*b^2*x^(5/2)*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - ((84*im)*b^2*x^(5/2)*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - (14*b^3*x^3*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (28*b*x^3*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (14*b^3*x^3*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (28*b*x^3*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (420*b^2*x^2*PolyLog(3, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^4) + (420*b^2*x^2*PolyLog(3, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^4) - ((84*im)*b^3*x^(5/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((168*im)*b*x^(5/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + ((84*im)*b^3*x^(5/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((168*im)*b*x^(5/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + ((1680*im)*b^2*x^(3/2)*PolyLog(4, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^5) + ((1680*im)*b^2*x^(3/2)*PolyLog(4, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^5) + (420*b^3*x^2*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^4) - (840*b*x^2*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^4) - (420*b^3*x^2*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^4) + (840*b*x^2*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^4) - (5040*b^2*x*PolyLog(5, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^6) - (5040*b^2*x*PolyLog(5, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^6) + ((1680*im)*b^3*x^(3/2)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^5) - ((3360*im)*b*x^(3/2)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^5) - ((1680*im)*b^3*x^(3/2)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^5) + ((3360*im)*b*x^(3/2)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^5) - ((10080*im)*b^2*sqrt(x)*PolyLog(6, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^7) - ((10080*im)*b^2*sqrt(x)*PolyLog(6, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^7) - (5040*b^3*x*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^6) + (10080*b*x*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^6) + (5040*b^3*x*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^6) - (10080*b*x*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^6) + (10080*b^2*PolyLog(7, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^8) + (10080*b^2*PolyLog(7, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^8) - ((10080*im)*b^3*sqrt(x)*PolyLog(7, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^7) + ((20160*im)*b*sqrt(x)*PolyLog(7, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^7) + ((10080*im)*b^3*sqrt(x)*PolyLog(7, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^7) - ((20160*im)*b*sqrt(x)*PolyLog(7, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^7) + (10080*b^3*PolyLog(8, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^8) - (20160*b*PolyLog(8, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^8) - (10080*b^3*PolyLog(8, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^8) + (20160*b*PolyLog(8, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^8) - (2*b^2*x^(7/2)*cos(c + d*sqrt(x)))/(a*(a^2 - b^2)*d*(b + a*sin(c + d*sqrt(x))))]
    @test_int [x^2/(a + b*csc(c + d*sqrt(x)))^2, x, 49, ((-2*im)*b^2*x^(5/2))/(a^2*(a^2 - b^2)*d) + x^3/(3*a^2) + (10*b^2*x^2*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) + (10*b^2*x^2*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) - ((2*im)*b^3*x^(5/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*im)*b*x^(5/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) + ((2*im)*b^3*x^(5/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*im)*b*x^(5/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) - ((40*im)*b^2*x^(3/2)*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - ((40*im)*b^2*x^(3/2)*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - (10*b^3*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (20*b*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (10*b^3*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (20*b*x^2*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (120*b^2*x*PolyLog(3, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^4) + (120*b^2*x*PolyLog(3, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^4) - ((40*im)*b^3*x^(3/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((80*im)*b*x^(3/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + ((40*im)*b^3*x^(3/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((80*im)*b*x^(3/2)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + ((240*im)*b^2*sqrt(x)*PolyLog(4, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^5) + ((240*im)*b^2*sqrt(x)*PolyLog(4, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^5) + (120*b^3*x*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^4) - (240*b*x*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^4) - (120*b^3*x*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^4) + (240*b*x*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^4) - (240*b^2*PolyLog(5, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^6) - (240*b^2*PolyLog(5, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^6) + ((240*im)*b^3*sqrt(x)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^5) - ((480*im)*b*sqrt(x)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^5) - ((240*im)*b^3*sqrt(x)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^5) + ((480*im)*b*sqrt(x)*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^5) - (240*b^3*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^6) + (480*b*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^6) + (240*b^3*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^6) - (480*b*PolyLog(6, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^6) - (2*b^2*x^(5/2)*cos(c + d*sqrt(x)))/(a*(a^2 - b^2)*d*(b + a*sin(c + d*sqrt(x))))]
    @test_int [x/(a + b*csc(c + d*sqrt(x)))^2, x, 37, ((-2*im)*b^2*x^(3/2))/(a^2*(a^2 - b^2)*d) + x^2/(2*a^2) + (6*b^2*x*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) + (6*b^2*x*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) - ((2*im)*b^3*x^(3/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*im)*b*x^(3/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) + ((2*im)*b^3*x^(3/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*im)*b*x^(3/2)*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) - ((12*im)*b^2*sqrt(x)*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - ((12*im)*b^2*sqrt(x)*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - (6*b^3*x*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (12*b*x*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (6*b^3*x*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (12*b*x*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (12*b^2*PolyLog(3, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^4) + (12*b^2*PolyLog(3, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^4) - ((12*im)*b^3*sqrt(x)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((24*im)*b*sqrt(x)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + ((12*im)*b^3*sqrt(x)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((24*im)*b*sqrt(x)*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + (12*b^3*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^4) - (24*b*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^4) - (12*b^3*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^4) + (24*b*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^4) - (2*b^2*x^(3/2)*cos(c + d*sqrt(x)))/(a*(a^2 - b^2)*d*(b + a*sin(c + d*sqrt(x))))]
    @test_int [1/(x*(a + b*csc(c + d*sqrt(x)))^2), x, 0, Unintegrable(1/(x*(a + b*csc(c + d*sqrt(x)))^2), x)]
    @test_int [1/(x^2*(a + b*csc(c + d*sqrt(x)))^2), x, 0, Unintegrable(1/(x^2*(a + b*csc(c + d*sqrt(x)))^2), x)]


    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*csc(c+d*x^(1/2)))^p=#


    #= ::Subsubsection::Closed:: =#
    #=p>0=#


    @test_int [x^(3/2)*(a + b*csc(c + d*sqrt(x))), x, 14, (2*a*x^(5/2))/5 - (4*b*x^2*atanh(ℯ^(im*(c + d*sqrt(x)))))/d + ((8*im)*b*x^(3/2)*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((8*im)*b*x^(3/2)*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - (24*b*x*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (24*b*x*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3 - ((48*im)*b*sqrt(x)*PolyLog(4, -ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((48*im)*b*sqrt(x)*PolyLog(4, ℯ^(im*(c + d*sqrt(x)))))/d^4 + (48*b*PolyLog(5, -ℯ^(im*(c + d*sqrt(x)))))/d^5 - (48*b*PolyLog(5, ℯ^(im*(c + d*sqrt(x)))))/d^5]
    @test_int [sqrt(x)*(a + b*csc(c + d*sqrt(x))), x, 10, (2*a*x^(3/2))/3 - (4*b*x*atanh(ℯ^(im*(c + d*sqrt(x)))))/d + ((4*im)*b*sqrt(x)*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((4*im)*b*sqrt(x)*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - (4*b*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (4*b*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3]
    @test_int [(a + b*csc(c + d*sqrt(x)))/sqrt(x), x, 4, 2*a*sqrt(x) - (2*b*atanh(cos(c + d*sqrt(x))))/d]
    @test_int [(a + b*csc(c + d*sqrt(x)))/x^(3/2), x, 2, (-2*a)/sqrt(x) + b*Unintegrable(csc(c + d*sqrt(x))/x^(3/2), x)]
    @test_int [(a + b*csc(c + d*sqrt(x)))/x^(5/2), x, 2, (-2*a)/(3*x^(3/2)) + b*Unintegrable(csc(c + d*sqrt(x))/x^(5/2), x)]


    @test_int [x^(3/2)*(a + b*csc(c + d*sqrt(x)))^2, x, 21, ((-2*im)*b^2*x^2)/d + (2*a^2*x^(5/2))/5 - (8*a*b*x^2*atanh(ℯ^(im*(c + d*sqrt(x)))))/d - (2*b^2*x^2*cot(c + d*sqrt(x)))/d + (8*b^2*x^(3/2)*log(1 - ℯ^((2*im)*(c + d*sqrt(x)))))/d^2 + ((16*im)*a*b*x^(3/2)*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((16*im)*a*b*x^(3/2)*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((12*im)*b^2*x*PolyLog(2, ℯ^((2*im)*(c + d*sqrt(x)))))/d^3 - (48*a*b*x*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (48*a*b*x*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3 + (12*b^2*sqrt(x)*PolyLog(3, ℯ^((2*im)*(c + d*sqrt(x)))))/d^4 - ((96*im)*a*b*sqrt(x)*PolyLog(4, -ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((96*im)*a*b*sqrt(x)*PolyLog(4, ℯ^(im*(c + d*sqrt(x)))))/d^4 + ((6*im)*b^2*PolyLog(4, ℯ^((2*im)*(c + d*sqrt(x)))))/d^5 + (96*a*b*PolyLog(5, -ℯ^(im*(c + d*sqrt(x)))))/d^5 - (96*a*b*PolyLog(5, ℯ^(im*(c + d*sqrt(x)))))/d^5]
    @test_int [sqrt(x)*(a + b*csc(c + d*sqrt(x)))^2, x, 15, ((-2*im)*b^2*x)/d + (2*a^2*x^(3/2))/3 - (8*a*b*x*atanh(ℯ^(im*(c + d*sqrt(x)))))/d - (2*b^2*x*cot(c + d*sqrt(x)))/d + (4*b^2*sqrt(x)*log(1 - ℯ^((2*im)*(c + d*sqrt(x)))))/d^2 + ((8*im)*a*b*sqrt(x)*PolyLog(2, -ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((8*im)*a*b*sqrt(x)*PolyLog(2, ℯ^(im*(c + d*sqrt(x)))))/d^2 - ((2*im)*b^2*PolyLog(2, ℯ^((2*im)*(c + d*sqrt(x)))))/d^3 - (8*a*b*PolyLog(3, -ℯ^(im*(c + d*sqrt(x)))))/d^3 + (8*a*b*PolyLog(3, ℯ^(im*(c + d*sqrt(x)))))/d^3]
    @test_int [(a + b*csc(c + d*sqrt(x)))^2/sqrt(x), x, 5, 2*a^2*sqrt(x) - (4*a*b*atanh(cos(c + d*sqrt(x))))/d - (2*b^2*cot(c + d*sqrt(x)))/d]
    @test_int [(a + b*csc(c + d*sqrt(x)))^2/x^(3/2), x, 0, Unintegrable((a + b*csc(c + d*sqrt(x)))^2/x^(3/2), x)]
    @test_int [(a + b*csc(c + d*sqrt(x)))^2/x^(5/2), x, 0, Unintegrable((a + b*csc(c + d*sqrt(x)))^2/x^(5/2), x)]


    @test_int [csc(sqrt(x))^3/sqrt(x), x, 3, -atanh(cos(sqrt(x))) - cot(sqrt(x))*csc(sqrt(x))]


    #= ::Subsubsection::Closed:: =#
    #=p<0=#


    @test_int [x^(3/2)/(a + b*csc(c + d*sqrt(x))), x, 17, (2*x^(5/2))/(5*a) + ((2*im)*b*x^2*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) - ((2*im)*b*x^2*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) + (8*b*x^(3/2)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) - (8*b*x^(3/2)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) + ((24*im)*b*x*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - ((24*im)*b*x*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - (48*b*sqrt(x)*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^4) + (48*b*sqrt(x)*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^4) - ((48*im)*b*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^5) + ((48*im)*b*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^5)]
    @test_int [sqrt(x)/(a + b*csc(c + d*sqrt(x))), x, 13, (2*x^(3/2))/(3*a) + ((2*im)*b*x*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) - ((2*im)*b*x*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d) + (4*b*sqrt(x)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) - (4*b*sqrt(x)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2) + ((4*im)*b*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3) - ((4*im)*b*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3)]
    @test_int [1/(sqrt(x)*(a + b*csc(c + d*sqrt(x)))), x, 5, (2*sqrt(x))/a + (4*b*atanh((a + b*tan((c + d*sqrt(x))/2))/sqrt(a^2 - b^2)))/(a*sqrt(a^2 - b^2)*d)]
    @test_int [1/(x^(3/2)*(a + b*csc(c + d*sqrt(x)))), x, 0, Unintegrable(1/(x^(3/2)*(a + b*csc(c + d*sqrt(x)))), x)]
    @test_int [1/(x^(5/2)*(a + b*csc(c + d*sqrt(x)))), x, 0, Unintegrable(1/(x^(5/2)*(a + b*csc(c + d*sqrt(x)))), x)]


    @test_int [x^(3/2)/(a + b*csc(c + d*sqrt(x)))^2, x, 43, ((-2*im)*b^2*x^2)/(a^2*(a^2 - b^2)*d) + (2*x^(5/2))/(5*a^2) + (8*b^2*x^(3/2)*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) + (8*b^2*x^(3/2)*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) - ((2*im)*b^3*x^2*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*im)*b*x^2*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) + ((2*im)*b^3*x^2*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*im)*b*x^2*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) - ((24*im)*b^2*x*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - ((24*im)*b^2*x*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - (8*b^3*x^(3/2)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (16*b*x^(3/2)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (8*b^3*x^(3/2)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (16*b*x^(3/2)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (48*b^2*sqrt(x)*PolyLog(3, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^4) + (48*b^2*sqrt(x)*PolyLog(3, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^4) - ((24*im)*b^3*x*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((48*im)*b*x*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + ((24*im)*b^3*x*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((48*im)*b*x*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + ((48*im)*b^2*PolyLog(4, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^5) + ((48*im)*b^2*PolyLog(4, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^5) + (48*b^3*sqrt(x)*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^4) - (96*b*sqrt(x)*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^4) - (48*b^3*sqrt(x)*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^4) + (96*b*sqrt(x)*PolyLog(4, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^4) + ((48*im)*b^3*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^5) - ((96*im)*b*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^5) - ((48*im)*b^3*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^5) + ((96*im)*b*PolyLog(5, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^5) - (2*b^2*x^2*cos(c + d*sqrt(x)))/(a*(a^2 - b^2)*d*(b + a*sin(c + d*sqrt(x))))]
    @test_int [sqrt(x)/(a + b*csc(c + d*sqrt(x)))^2, x, 31, ((-2*im)*b^2*x)/(a^2*(a^2 - b^2)*d) + (2*x^(3/2))/(3*a^2) + (4*b^2*sqrt(x)*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) + (4*b^2*sqrt(x)*log(1 + (a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2))))/(a^2*(a^2 - b^2)*d^2) - ((2*im)*b^3*x*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*im)*b*x*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) + ((2*im)*b^3*x*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*im)*b*x*log(1 - (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d) - ((4*im)*b^2*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b - sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - ((4*im)*b^2*PolyLog(2, -((a*ℯ^(im*(c + d*sqrt(x))))/(im*b + sqrt(a^2 - b^2)))))/(a^2*(a^2 - b^2)*d^3) - (4*b^3*sqrt(x)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (8*b*sqrt(x)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) + (4*b^3*sqrt(x)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (8*b*sqrt(x)*PolyLog(2, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2) - ((4*im)*b^3*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((8*im)*b*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) + ((4*im)*b^3*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((8*im)*b*PolyLog(3, (im*a*ℯ^(im*(c + d*sqrt(x))))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^3) - (2*b^2*x*cos(c + d*sqrt(x)))/(a*(a^2 - b^2)*d*(b + a*sin(c + d*sqrt(x))))]
    @test_int [1/(sqrt(x)*(a + b*csc(c + d*sqrt(x)))^2), x, 7, (2*sqrt(x))/a^2 + (4*b*(2*a^2 - b^2)*atanh((a + b*tan((c + d*sqrt(x))/2))/sqrt(a^2 - b^2)))/(a^2*(a^2 - b^2)^(3/2)*d) - (2*b^2*cot(c + d*sqrt(x)))/(a*(a^2 - b^2)*d*(a + b*csc(c + d*sqrt(x))))]
    @test_int [1/(x^(3/2)*(a + b*csc(c + d*sqrt(x)))^2), x, 0, Unintegrable(1/(x^(3/2)*(a + b*csc(c + d*sqrt(x)))^2), x)]
    @test_int [1/(x^(5/2)*(a + b*csc(c + d*sqrt(x)))^2), x, 0, Unintegrable(1/(x^(5/2)*(a + b*csc(c + d*sqrt(x)))^2), x)]


    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*csc(c+d*x^n))^p=#


    @test_int [(e*x)^m*(a + b*csc(c + d*x^n))^p, x, 1, ((e*x)^m*Unintegrable(x^m*(a + b*csc(c + d*x^n))^p, x))/x^m]


    #= ::Subsubsection::Closed:: =#
    #=p>0=#


    @test_int [(e*x)^(-1 + n)*(a + b*csc(c + d*x^n)), x, 5, (a*(e*x)^n)/(e*n) - (b*(e*x)^n*atanh(cos(c + d*x^n)))/(d*e*n*x^n)]
    @test_int [(e*x)^(-1 + 2*n)*(a + b*csc(c + d*x^n)), x, 9, (a*(e*x)^(2*n))/(2*e*n) - (2*b*(e*x)^(2*n)*atanh(ℯ^(im*(c + d*x^n))))/(d*e*n*x^n) + (im*b*(e*x)^(2*n)*PolyLog(2, -ℯ^(im*(c + d*x^n))))/(d^2*e*n*x^(2*n)) - (im*b*(e*x)^(2*n)*PolyLog(2, ℯ^(im*(c + d*x^n))))/(d^2*e*n*x^(2*n))]
    @test_int [(e*x)^(-1 + 3*n)*(a + b*csc(c + d*x^n)), x, 11, (a*(e*x)^(3*n))/(3*e*n) - (2*b*(e*x)^(3*n)*atanh(ℯ^(im*(c + d*x^n))))/(d*e*n*x^n) + ((2*im)*b*(e*x)^(3*n)*PolyLog(2, -ℯ^(im*(c + d*x^n))))/(d^2*e*n*x^(2*n)) - ((2*im)*b*(e*x)^(3*n)*PolyLog(2, ℯ^(im*(c + d*x^n))))/(d^2*e*n*x^(2*n)) - (2*b*(e*x)^(3*n)*PolyLog(3, -ℯ^(im*(c + d*x^n))))/(d^3*e*n*x^(3*n)) + (2*b*(e*x)^(3*n)*PolyLog(3, ℯ^(im*(c + d*x^n))))/(d^3*e*n*x^(3*n))]


    @test_int [(e*x)^(-1 + n)*(a + b*csc(c + d*x^n))^2, x, 6, (a^2*(e*x)^n)/(e*n) - (2*a*b*(e*x)^n*atanh(cos(c + d*x^n)))/(d*e*n*x^n) - (b^2*(e*x)^n*cot(c + d*x^n))/(d*e*n*x^n)]
    @test_int [(e*x)^(-1 + 2*n)*(a + b*csc(c + d*x^n))^2, x, 11, (a^2*(e*x)^(2*n))/(2*e*n) - (4*a*b*(e*x)^(2*n)*atanh(ℯ^(im*(c + d*x^n))))/(d*e*n*x^n) - (b^2*(e*x)^(2*n)*cot(c + d*x^n))/(d*e*n*x^n) + (b^2*(e*x)^(2*n)*log(sin(c + d*x^n)))/(d^2*e*n*x^(2*n)) + ((2*im)*a*b*(e*x)^(2*n)*PolyLog(2, -ℯ^(im*(c + d*x^n))))/(d^2*e*n*x^(2*n)) - ((2*im)*a*b*(e*x)^(2*n)*PolyLog(2, ℯ^(im*(c + d*x^n))))/(d^2*e*n*x^(2*n))]
    @test_int [(e*x)^(-1 + 3*n)*(a + b*csc(c + d*x^n))^2, x, 16, (a^2*(e*x)^(3*n))/(3*e*n) - (im*b^2*(e*x)^(3*n))/(d*e*n*x^n) - (4*a*b*(e*x)^(3*n)*atanh(ℯ^(im*(c + d*x^n))))/(d*e*n*x^n) - (b^2*(e*x)^(3*n)*cot(c + d*x^n))/(d*e*n*x^n) + (2*b^2*(e*x)^(3*n)*log(1 - ℯ^((2*im)*(c + d*x^n))))/(d^2*e*n*x^(2*n)) + ((4*im)*a*b*(e*x)^(3*n)*PolyLog(2, -ℯ^(im*(c + d*x^n))))/(d^2*e*n*x^(2*n)) - ((4*im)*a*b*(e*x)^(3*n)*PolyLog(2, ℯ^(im*(c + d*x^n))))/(d^2*e*n*x^(2*n)) - (im*b^2*(e*x)^(3*n)*PolyLog(2, ℯ^((2*im)*(c + d*x^n))))/(d^3*e*n*x^(3*n)) - (4*a*b*(e*x)^(3*n)*PolyLog(3, -ℯ^(im*(c + d*x^n))))/(d^3*e*n*x^(3*n)) + (4*a*b*(e*x)^(3*n)*PolyLog(3, ℯ^(im*(c + d*x^n))))/(d^3*e*n*x^(3*n))]


    #= ::Subsubsection::Closed:: =#
    #=p<0=#


    @test_int [(e*x)^(-1 + n)/(a + b*csc(c + d*x^n)), x, 6, (e*x)^n/(a*e*n) + (2*b*(e*x)^n*atanh((a + b*tan((c + d*x^n)/2))/sqrt(a^2 - b^2)))/(a*sqrt(a^2 - b^2)*d*e*n*x^n)]
    @test_int [(e*x)^(-1 + 2*n)/(a + b*csc(c + d*x^n)), x, 12, (e*x)^(2*n)/(2*a*e*n) + (im*b*(e*x)^(2*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d*e*n*x^n) - (im*b*(e*x)^(2*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d*e*n*x^n) + (b*(e*x)^(2*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2*e*n*x^(2*n)) - (b*(e*x)^(2*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2*e*n*x^(2*n))]
    @test_int [(e*x)^(-1 + 3*n)/(a + b*csc(c + d*x^n)), x, 14, (e*x)^(3*n)/(3*a*e*n) + (im*b*(e*x)^(3*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d*e*n*x^n) - (im*b*(e*x)^(3*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d*e*n*x^n) + (2*b*(e*x)^(3*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2*e*n*x^(2*n)) - (2*b*(e*x)^(3*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^2*e*n*x^(2*n)) + ((2*im)*b*(e*x)^(3*n)*PolyLog(3, (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3*e*n*x^(3*n)) - ((2*im)*b*(e*x)^(3*n)*PolyLog(3, (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(a*sqrt(-a^2 + b^2)*d^3*e*n*x^(3*n))]


    @test_int [(e*x)^(-1 + n)/(a + b*csc(c + d*x^n))^2, x, 8, (e*x)^n/(a^2*e*n) + (2*b*(2*a^2 - b^2)*(e*x)^n*atanh((a + b*tan((c + d*x^n)/2))/sqrt(a^2 - b^2)))/(a^2*(a^2 - b^2)^(3/2)*d*e*n*x^n) - (b^2*(e*x)^n*cot(c + d*x^n))/(a*(a^2 - b^2)*d*e*n*x^n*(a + b*csc(c + d*x^n)))]
    @test_int [(e*x)^(-1 + 2*n)/(a + b*csc(c + d*x^n))^2, x, 23, (e*x)^(2*n)/(2*a^2*e*n) - (im*b^3*(e*x)^(2*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d*e*n*x^n) + ((2*im)*b*(e*x)^(2*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d*e*n*x^n) + (im*b^3*(e*x)^(2*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d*e*n*x^n) - ((2*im)*b*(e*x)^(2*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d*e*n*x^n) + (b^2*(e*x)^(2*n)*log(b + a*sin(c + d*x^n)))/(a^2*(a^2 - b^2)*d^2*e*n*x^(2*n)) - (b^3*(e*x)^(2*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2*e*n*x^(2*n)) + (2*b*(e*x)^(2*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2*e*n*x^(2*n)) + (b^3*(e*x)^(2*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(a^2*(-a^2 + b^2)^(3/2)*d^2*e*n*x^(2*n)) - (2*b*(e*x)^(2*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(a^2*sqrt(-a^2 + b^2)*d^2*e*n*x^(2*n)) - (b^2*(e*x)^(2*n)*cos(c + d*x^n))/(a*(a^2 - b^2)*d*e*n*x^n*(b + a*sin(c + d*x^n)))]
    @test_int [(e*x)^(-1 + 3*n)/(a + b*csc(c + d*x^n))^2, x, 32, (e*x)^(3*n)/(3*a^2*e*n) - (im*b^2*(e*x)^(3*n))/(x^n*(a^2*(a^2 - b^2)*d*e*n)) + (2*b^2*(e*x)^(3*n)*log(1 + (a*ℯ^(im*(c + d*x^n)))/(im*b - sqrt(a^2 - b^2))))/(x^(2*n)*(a^2*(a^2 - b^2)*d^2*e*n)) + (2*b^2*(e*x)^(3*n)*log(1 + (a*ℯ^(im*(c + d*x^n)))/(im*b + sqrt(a^2 - b^2))))/(x^(2*n)*(a^2*(a^2 - b^2)*d^2*e*n)) - (im*b^3*(e*x)^(3*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(x^n*(a^2*(-a^2 + b^2)^(3/2)*d*e*n)) + (2*im*b*(e*x)^(3*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(x^n*(a^2*sqrt(-a^2 + b^2)*d*e*n)) + (im*b^3*(e*x)^(3*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(x^n*(a^2*(-a^2 + b^2)^(3/2)*d*e*n)) - (2*im*b*(e*x)^(3*n)*log(1 - (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(x^n*(a^2*sqrt(-a^2 + b^2)*d*e*n)) - (2*im*b^2*(e*x)^(3*n)*PolyLog(2, -((a*ℯ^(im*(c + d*x^n)))/(im*b - sqrt(a^2 - b^2)))))/(x^(3*n)*(a^2*(a^2 - b^2)*d^3*e*n)) - (2*im*b^2*(e*x)^(3*n)*PolyLog(2, -((a*ℯ^(im*(c + d*x^n)))/(im*b + sqrt(a^2 - b^2)))))/(x^(3*n)*(a^2*(a^2 - b^2)*d^3*e*n)) - (2*b^3*(e*x)^(3*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(x^(2*n)*(a^2*(-a^2 + b^2)^(3/2)*d^2*e*n)) + (4*b*(e*x)^(3*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(x^(2*n)*(a^2*sqrt(-a^2 + b^2)*d^2*e*n)) + (2*b^3*(e*x)^(3*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(x^(2*n)*(a^2*(-a^2 + b^2)^(3/2)*d^2*e*n)) - (4*b*(e*x)^(3*n)*PolyLog(2, (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(x^(2*n)*(a^2*sqrt(-a^2 + b^2)*d^2*e*n)) - (2*im*b^3*(e*x)^(3*n)*PolyLog(3, (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(x^(3*n)*(a^2*(-a^2 + b^2)^(3/2)*d^3*e*n)) + (4*im*b*(e*x)^(3*n)*PolyLog(3, (im*a*ℯ^(im*(c + d*x^n)))/(b - sqrt(-a^2 + b^2))))/(x^(3*n)*(a^2*sqrt(-a^2 + b^2)*d^3*e*n)) + (2*im*b^3*(e*x)^(3*n)*PolyLog(3, (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(x^(3*n)*(a^2*(-a^2 + b^2)^(3/2)*d^3*e*n)) - (4*im*b*(e*x)^(3*n)*PolyLog(3, (im*a*ℯ^(im*(c + d*x^n)))/(b + sqrt(-a^2 + b^2))))/(x^(3*n)*(a^2*sqrt(-a^2 + b^2)*d^3*e*n)) - (b^2*(e*x)^(3*n)*cos(c + d*x^n))/(x^n*(a*(a^2 - b^2)*d*e*n*(b + a*sin(c + d*x^n))))]
    end
