Need help for taking an integral. Do not solve it, just check the solution???
610143
I think ur right cos^2(theta) should be cos(theta). then the answer would be perfect.
748051
The primitive of your integral is:\n\ns*(e^(st))*(1/w)*atan(s/w)\n\nYou have to do a trigonometric substitution to get there. Do not always trust the weird answers you get with complex calculators.
506663
That'll be the integral over C of k.curl(F)\ncurl(F) = 0i,-4j,-1k\nk.curl(F) = -1\narea of C = 9pi\ntherefore W = -9pi
297440
Are you looking for indefinite  integral   of x^(sin(1/x)) ?\n\nMathematica has a web site you can plug-in the integrant and get the result (if it exist in closed form)\n\nBy hand: try to break this power expression using log and exp functions. If  a=ln(b), then b=exp(a) and therefore b=exp(ln(b)).\n\nIn this way your integrant could be written as \n\nexp(ln(integrand))\nand since it is of power form, use the properties of ln and exp functions to break it down and thus reduce it to simpler integrals.
815728
first this is not a PDE but ODE\n\nsimple integration would do
786513
put x^2=t\n2xdx=dt\nxdx=1/2dt\nthe integral now is\n(1/2dt/1+t^2\n(1/2)tan^-1t+C\n=(1/2)tan^-1(x^2)+C
859250
integral = x*tan(x)+ln(sec(x))  (use integration by parts with du = sec^2(x) and v = x).\n\ng'(x) = f(x), so a, c, e and g are true (b is true if f is continuous)\n\nSteve
71557
integral of [x^y+y^x]dx= [x^(y+1)]/(y+1)+(y^x)*(1/ln y)+constant(if not definite)
798015
y=e^x - 1 cuts the x axis at x = 1 Thus the integral needs to be done in two parts as area is a scalar quantity not a vector.\n\nA = |∫(x = -3 to 0) (e^x - 1) dx| + |∫(x = 0 to 3)  (e^x - 1) dx|\n\n= | [e^x - x] (x = -3 to 0) | + | [e^x - x] (x = 0 to 3) |\n\n= |(e^0 - 0) - (e^(-3) - -3)| + |(e^(3) - 3) - (e^0 - 0)| \n\n= 2 + e^(-3) + e^3 - 4\n\n= e^3 + e^(-3) - 2\n\n≈ 18.14 units²
765864
I'm unclear with the way you stated the problem. Am I looking for a implicit derivative. I'll check back to solve it.
611207
The only way to do this is by using the reduction formula for int(sin(x)^n), which is valid for n>0.  Unfortuantely, it reduces to another integral for sin(x)^(n-2), for which the reduction formula no longer is valid.  Hence, the only way to do this integral is by using numerical integration techniques.\n\nProbably the best way to do this problem is to convert sin(x)^(1/2) to a taylor series.  \n\nI did this and got:\nx^0.5 - x^2.5/12 + x^4.5/1440 - x^6.5/24192 - 67/29030400*x^8.5 .....\n\nIntegrate:\n\n(2/3)*x^(3/2)-(1/42)*x^(7/2)+(1/7920)*x^(11/2)-(1/181440)*x^(15/2)-(67/275788800)*x^(19/2)......\n\nNeedless to say, after the first 4 terms, any error from a direct integration of sqrt(sin(x) is less than 10^-6, which I would say is pretty damn close.  \n\nThere ya go...
1092533
The previous person almost got there.\nThe indefinite integral is (1+x)[log(1+x) - 1] + C\n\nSubstitute x=1 to get 2[log(2) - 1] + C\nSubstitute x=0 to get  -1 + C.\n\nThe definite integral is \n2[log(2) - 1]  - [-1]\n= 2log(2) -1\n=log(4) - 1\n=log(4) - log(e)\n=log(4/e)
894395
∞\n\nConsider that this function is everywhere positive, and that as the lower bound of the integral increases, the function being integrated does not approach zero (in fact, it becomes increasingly large), so the integral of e^(y²) from -∞ to anything must in fact be infinite.
880047
I can find this on a TI-84+, is that how you want to get it or do you need an algebraic solution?
979363
You can't do this integral straight-up because it is a special case.  The integral is:\n\nsqrt(pi/2)Fresnel(sqrt(2/pi)x)\n\nBelow are websites with an Integral Calculator and the Fresnel function\n\n-------\n\nHope this helps
400264
split the integral up\n\nyou have:\n(1-2x^2)/x = 1/x - 2x^2/x = 1/x - 2x\n\nintegrating this gives:\n\nIn(x) - 2x^2/2 = In(x)-x^2
195201
i think u typed the question wrong, can u please correct it and if u have 2 unknowns, please give 2 equations, else u cant get a definite solution