text:
using Rubin
using Tests
using Elliptic
using HypergeometricFunctions
using Polylogarithms
using SpecialFunctions

@test integrate(x^3*(a+b*arctan(c*x))*(d+im*c*d*x), x) == :(1//4*d*x^4*(a+b*arctan(c*x))+-1//4*b*d*c^-4*arctan(c*x)+-1//12*b*d*c^-1*x^3+-1//20*im*b*d*x^4+1//4*b*d*x*c^-3+-1//10*im*b*d*c^-4*log(1+c^2*x^2)+1//5*im*c*d*x^5*(a+b*arctan(c*x))+1//10*im*b*d*c^-2*x^2)
@test integrate(x^2*(a+b*arctan(c*x))*(d+im*c*d*x), x) == :(1//3*d*x^3*(a+b*arctan(c*x))+-1//6*b*d*c^-1*x^2+-1//12*im*b*d*x^3+1//6*b*d*c^-3*log(1+c^2*x^2)+-1//4*im*b*d*c^-3*arctan(c*x)+1//4*im*b*d*x*c^-2+1//4*im*c*d*x^4*(a+b*arctan(c*x)))
@test integrate(x*(a+b*arctan(c*x))*(d+im*c*d*x), x) == :((1/2)*d*x^2*(a+b*arctan(c*x))+(1/2)*b*d*c^-2*arctan(c*x)+-1//2*b*d*x*c^-1+-1//6*im*b*d*x^2+1//3*im*c*d*x^3*(a+b*arctan(c*x))+1//6*im*b*d*c^-2*log(1+c^2*x^2))
@test integrate((a+b*arctan(c*x))*(d+im*c*d*x), x) == :(-1*b*d*c^-1*log(im+c*x)+-1//2*im*b*d*x+-1//2*im*d*c^-1*(1+im*c*x)^2*(a+b*arctan(c*x)))
@test integrate(x^-1*(a+b*arctan(c*x))*(d+im*c*d*x), x) == :(a*d*log(x)+(1/2)*im*b*d*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*d*Polylogarithms.polylog(2,im*c*x)+-1//2*im*b*d*log(1+c^2*x^2)+im*a*c*d*x+im*b*c*d*x*arctan(c*x))
@test integrate(x^-2*(a+b*arctan(c*x))*(d+im*c*d*x), x) == :(-1*d*x^-1*(a+b*arctan(c*x))+b*c*d*log(x)+(1/2)*b*c*d*Polylogarithms.polylog(2,im*c*x)+-1//2*b*c*d*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*b*c*d*log(1+c^2*x^2)+im*a*c*d*log(x))
@test integrate(x^-3*(a+b*arctan(c*x))*(d+im*c*d*x), x) == :(-1//2*b*c*d*x^-1+-1//2*d*x^-2*(1+im*c*x)^2*(a+b*arctan(c*x))+im*b*d*c^2*log(x)+-1*im*b*d*c^2*log(im+c*x))
@test integrate(x^-4*(a+b*arctan(c*x))*(d+im*c*d*x), x) == :(-1//3*d*x^-3*(a+b*arctan(c*x))+-1//3*b*d*c^3*log(x)+-1//6*b*c*d*x^-2+-1//12*b*d*c^3*log(im+-1*c*x)+5//12*b*d*c^3*log(im+c*x)+-1//2*im*b*d*c^2*x^-1+-1//2*im*c*d*x^-2*(a+b*arctan(c*x)))
@test integrate(x^-5*(a+b*arctan(c*x))*(d+im*c*d*x), x) == :(-1//4*d*x^-4*(a+b*arctan(c*x))+-1//12*b*c*d*x^-3+1//4*b*d*c^3*x^-1+-1//3*im*b*d*c^4*log(x)+-1//3*im*c*d*x^-3*(a+b*arctan(c*x))+-1//6*im*b*d*c^2*x^-2+1//24*im*b*d*c^4*log(im+-1*c*x)+7//24*im*b*d*c^4*log(im+c*x))
@test integrate(x^3*(d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :(1//4*d^2*x^4*(a+b*arctan(c*x))+-5//12*b*c^-4*d^2*arctan(c*x)+-5//36*b*c^-1*d^2*x^3+-1//6*c^2*d^2*x^6*(a+b*arctan(c*x))+-1//10*im*b*d^2*x^4+1//30*b*c*d^2*x^5+5//12*b*x*c^-3*d^2+-1//5*im*b*c^-4*d^2*log(1+c^2*x^2)+1//5*im*b*c^-2*d^2*x^2+2//5*im*c*d^2*x^5*(a+b*arctan(c*x)))
@test integrate(x^2*(d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :(1//3*d^2*x^3*(a+b*arctan(c*x))+-4//15*b*c^-1*d^2*x^2+-1//5*c^2*d^2*x^5*(a+b*arctan(c*x))+-1//6*im*b*d^2*x^3+1//20*b*c*d^2*x^4+4//15*b*c^-3*d^2*log(1+c^2*x^2)+(1/2)*im*b*x*c^-2*d^2+(1/2)*im*c*d^2*x^4*(a+b*arctan(c*x))+-1//2*im*b*c^-3*d^2*arctan(c*x))
@test integrate(x*(d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :((1/2)*d^2*x^2*(a+b*arctan(c*x))+-3//4*b*x*c^-1*d^2+-1//3*im*b*d^2*x^2+-1//4*c^2*d^2*x^4*(a+b*arctan(c*x))+1//12*b*c*d^2*x^3+3//4*b*c^-2*d^2*arctan(c*x)+1//3*im*b*c^-2*d^2*log(1+c^2*x^2)+2//3*im*c*d^2*x^3*(a+b*arctan(c*x)))
@test integrate((d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :(-4//3*b*c^-1*d^2*log(1+-1*im*c*x)+-2//3*im*b*x*d^2+-1//6*b*c^-1*d^2*(1+im*c*x)^2+-1//3*im*c^-1*d^2*(1+im*c*x)^3*(a+b*arctan(c*x)))
@test integrate(x^-1*(d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :(a*d^2*log(x)+-1//2*b*d^2*arctan(c*x)+(1/2)*im*b*d^2*Polylogarithms.polylog(2,-1*im*c*x)+(1/2)*b*c*x*d^2+-1*im*b*d^2*log(1+c^2*x^2)+-1//2*im*b*d^2*Polylogarithms.polylog(2,im*c*x)+-1//2*c^2*d^2*x^2*(a+b*arctan(c*x))+2*im*a*c*x*d^2+2*im*b*c*x*d^2*arctan(c*x))
@test integrate(x^-2*(d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :(-1*d^2*x^-1*(a+b*arctan(c*x))+b*c*d^2*Polylogarithms.polylog(2,im*c*x)+b*c*d^2*log(x)+-1*a*x*c^2*d^2+-1*b*c*d^2*Polylogarithms.polylog(2,-1*im*c*x)+-1*b*x*c^2*d^2*arctan(c*x)+2*im*a*c*d^2*log(x))
@test integrate(x^-3*(d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :(-1//2*d^2*x^-2*(a+b*arctan(c*x))+-1*a*c^2*d^2*log(x)+-1//2*b*c*d^2*x^-1+-1//2*b*c^2*d^2*arctan(c*x)+(1/2)*im*b*c^2*d^2*Polylogarithms.polylog(2,im*c*x)+-1*im*b*c^2*d^2*log(1+c^2*x^2)+-2*im*c*d^2*x^-1*(a+b*arctan(c*x))+2*im*b*c^2*d^2*log(x)+-1//2*im*b*c^2*d^2*Polylogarithms.polylog(2,-1*im*c*x))
@test integrate(x^-4*(d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :(-4//3*b*c^3*d^2*log(x)+-1//3*d^2*x^-3*(1+im*c*x)^3*(a+b*arctan(c*x))+-1//6*b*c*d^2*x^-2+4//3*b*c^3*d^2*log(im+c*x)+-1*im*b*c^2*d^2*x^-1)
@test integrate(x^-5*(d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :(-1//4*d^2*x^-4*(a+b*arctan(c*x))+(1/2)*c^2*d^2*x^-2*(a+b*arctan(c*x))+-1//12*b*c*d^2*x^-3+3//4*b*c^3*d^2*x^-1+-2//3*im*b*c^4*d^2*log(x)+-2//3*im*c*d^2*x^-3*(a+b*arctan(c*x))+-1//3*im*b*c^2*d^2*x^-2+-1//24*im*b*c^4*d^2*log(im+-1*c*x)+17//24*im*b*c^4*d^2*log(im+c*x))
@test integrate(x^-6*(d+im*c*d*x)^2*(a+b*arctan(c*x)), x) == :(-1//5*d^2*x^-5*(a+b*arctan(c*x))+-31//60*b*c^5*d^2*log(im+c*x)+-1//20*b*c*d^2*x^-4+-1//60*b*c^5*d^2*log(im+-1*c*x)+1//3*c^2*d^2*x^-3*(a+b*arctan(c*x))+4//15*b*c^3*d^2*x^-2+8//15*b*c^5*d^2*log(x)+(1/2)*im*b*c^4*d^2*x^-1+-1//2*im*c*d^2*x^-4*(a+b*arctan(c*x))+-1//6*im*b*c^2*d^2*x^-3)
@test integrate(x^3*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(1//4*d^3*x^4*(a+b*arctan(c*x))+-13//70*im*b*d^3*x^4+-3//4*b*c^-4*d^3*arctan(c*x)+-1//2*c^2*d^3*x^6*(a+b*arctan(c*x))+-1//4*b*c^-1*d^3*x^3+1//10*b*c*d^3*x^5+3//4*b*x*c^-3*d^3+-13//35*im*b*c^-4*d^3*log(1+c^2*x^2)+-1//7*im*c^3*d^3*x^7*(a+b*arctan(c*x))+1//42*im*b*c^2*d^3*x^6+3//5*im*c*d^3*x^5*(a+b*arctan(c*x))+13//35*im*b*c^-2*d^3*x^2)
@test integrate(x^2*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(1//3*d^3*x^3*(a+b*arctan(c*x))+-11//36*im*b*d^3*x^3+-7//15*b*c^-1*d^3*x^2+-3//5*c^2*d^3*x^5*(a+b*arctan(c*x))+3//20*b*c*d^3*x^4+7//15*b*c^-3*d^3*log(1+c^2*x^2)+-11//12*im*b*c^-3*d^3*arctan(c*x)+-1//6*im*c^3*d^3*x^6*(a+b*arctan(c*x))+1//30*im*b*c^2*d^3*x^5+3//4*im*c*d^3*x^4*(a+b*arctan(c*x))+11//12*im*b*x*c^-2*d^3)
@test integrate(x*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(-3//5*b*x*c^-1*d^3+-1//5*c^-2*d^3*(1+im*c*x)^5*(a+b*arctan(c*x))+-1//20*b*c^-2*d^3*(im+-1*c*x)^3+1//4*c^-2*d^3*(1+im*c*x)^4*(a+b*arctan(c*x))+-3//20*im*b*c^-2*d^3*(im+-1*c*x)^2+1//20*im*b*c^-2*d^3*(im+-1*c*x)^4+6//5*im*b*c^-2*d^3*log(im+c*x))
@test integrate((d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(-1*im*b*x*d^3+-2*b*c^-1*d^3*log(1+-1*im*c*x)+-1//4*b*c^-1*d^3*(1+im*c*x)^2+-1//12*b*c^-1*d^3*(1+im*c*x)^3+-1//4*im*c^-1*d^3*(1+im*c*x)^4*(a+b*arctan(c*x)))
@test integrate(x^-1*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(a*d^3*log(x)+-3//2*b*d^3*arctan(c*x)+(1/2)*im*b*d^3*Polylogarithms.polylog(2,-1*im*c*x)+-5//3*im*b*d^3*log(1+c^2*x^2)+-3//2*c^2*d^3*x^2*(a+b*arctan(c*x))+-1//2*im*b*d^3*Polylogarithms.polylog(2,im*c*x)+3//2*b*c*x*d^3+3*im*a*c*x*d^3+-1//3*im*c^3*d^3*x^3*(a+b*arctan(c*x))+1//6*im*b*c^2*d^3*x^2+3*im*b*c*x*d^3*arctan(c*x))
@test integrate(x^-2*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(-1*d^3*x^-1*(a+b*arctan(c*x))+b*c*d^3*log(x)+b*c*d^3*log(1+c^2*x^2)+-3*a*x*c^2*d^3+-3//2*b*c*d^3*Polylogarithms.polylog(2,-1*im*c*x)+3//2*b*c*d^3*Polylogarithms.polylog(2,im*c*x)+(1/2)*im*b*x*c^2*d^3+-3*b*x*c^2*d^3*arctan(c*x)+3*im*a*c*d^3*log(x)+-1//2*im*b*c*d^3*arctan(c*x)+-1//2*im*c^3*d^3*x^2*(a+b*arctan(c*x)))
@test integrate(x^-3*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(-1//2*d^3*x^-2*(a+b*arctan(c*x))+-3*a*c^2*d^3*log(x)+-1//2*b*c*d^3*x^-1+-1//2*b*c^2*d^3*arctan(c*x)+-1*im*a*x*c^3*d^3+-1*im*b*c^2*d^3*log(1+c^2*x^2)+-3*im*c*d^3*x^-1*(a+b*arctan(c*x))+3*im*b*c^2*d^3*log(x)+-3//2*im*b*c^2*d^3*Polylogarithms.polylog(2,-1*im*c*x)+3//2*im*b*c^2*d^3*Polylogarithms.polylog(2,im*c*x)+-1*im*b*x*c^3*d^3*arctan(c*x))
@test integrate(x^-4*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(-1//3*d^3*x^-3*(a+b*arctan(c*x))+(1/2)*b*c^3*d^3*Polylogarithms.polylog(2,-1*im*c*x)+3*c^2*d^3*x^-1*(a+b*arctan(c*x))+-10//3*b*c^3*d^3*log(x)+-1//2*b*c^3*d^3*Polylogarithms.polylog(2,im*c*x)+-1//6*b*c*d^3*x^-2+5//3*b*c^3*d^3*log(1+c^2*x^2)+-1*im*a*c^3*d^3*log(x)+-3//2*im*b*c^2*d^3*x^-1+-3//2*im*b*c^3*d^3*arctan(c*x)+-3//2*im*c*d^3*x^-2*(a+b*arctan(c*x)))
@test integrate(x^-5*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(-1//4*d^3*x^-4*(1+im*c*x)^4*(a+b*arctan(c*x))+-1//12*b*c*d^3*x^-3+7//4*b*c^3*d^3*x^-1+-2*im*b*c^4*d^3*log(x)+2*im*b*c^4*d^3*log(im+c*x)+-1//2*im*b*c^2*d^3*x^-2)
@test integrate(x^-6*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(-6//5*b*c^5*d^3*log(im+c*x)+-1//5*d^3*x^-5*(1+im*c*x)^4*(a+b*arctan(c*x))+-1//20*b*c*d^3*x^-4+3//5*b*c^3*d^3*x^-2+6//5*b*c^5*d^3*log(x)+-1//4*im*b*c^2*d^3*x^-3+5//4*im*b*c^4*d^3*x^-1+1//20*im*c*d^3*x^-4*(1+im*c*x)^4*(a+b*arctan(c*x)))
@test integrate(x^-7*(d+im*c*d*x)^3*(a+b*arctan(c*x)), x) == :(-1//6*d^3*x^-6*(a+b*arctan(c*x))+-11//12*b*c^5*d^3*x^-1+-1//30*b*c*d^3*x^-5+3//4*c^2*d^3*x^-4*(a+b*arctan(c*x))+11//36*b*c^3*d^3*x^-3+-37//40*im*b*c^6*d^3*log(im+c*x)+-3//5*im*c*d^3*x^-5*(a+b*arctan(c*x))+-3//20*im*b*c^2*d^3*x^-4+-1//120*im*b*c^6*d^3*log(im+-1*c*x)+1//3*im*c^3*d^3*x^-3*(a+b*arctan(c*x))+7//15*im*b*c^4*d^3*x^-2+14//15*im*b*c^6*d^3*log(x))
@test integrate(x^3*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(1//4*d^4*x^4*(a+b*arctan(c*x))+-1*c^2*d^4*x^6*(a+b*arctan(c*x))+-12//35*im*b*d^4*x^4+-11//8*b*c^-4*d^4*arctan(c*x)+-11//24*b*c^-1*d^4*x^3+-1//56*b*c^3*d^4*x^7+1//8*c^4*d^4*x^8*(a+b*arctan(c*x))+9//40*b*c*d^4*x^5+11//8*b*x*c^-3*d^4+-24//35*im*b*c^-4*d^4*log(1+c^2*x^2)+-4//7*im*c^3*d^4*x^7*(a+b*arctan(c*x))+2//21*im*b*c^2*d^4*x^6+4//5*im*c*d^4*x^5*(a+b*arctan(c*x))+24//35*im*b*c^-2*d^4*x^2)
@test integrate(x^2*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-88//105*b*c^-1*d^4*x^2+-5//9*im*b*d^4*x^3+-1//42*b*c^3*d^4*x^6+47//140*b*c*d^4*x^4+176//105*b*c^-3*d^4*log(im+c*x)+-1//3*im*c^-3*d^4*(1+im*c*x)^6*(a+b*arctan(c*x))+1//5*im*c^-3*d^4*(1+im*c*x)^5*(a+b*arctan(c*x))+1//7*im*c^-3*d^4*(1+im*c*x)^7*(a+b*arctan(c*x))+2//15*im*b*c^2*d^4*x^5+5//3*im*b*x*c^-2*d^4)
@test integrate(x*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-16//15*b*x*c^-1*d^4+-4//45*b*c^-2*d^4*(im+-1*c*x)^3+-1//6*c^-2*d^4*(1+im*c*x)^6*(a+b*arctan(c*x))+1//5*c^-2*d^4*(1+im*c*x)^5*(a+b*arctan(c*x))+1//30*b*c^-2*d^4*(im+-1*c*x)^5+-4//15*im*b*c^-2*d^4*(im+-1*c*x)^2+1//30*im*b*c^-2*d^4*(im+-1*c*x)^4+32//15*im*b*c^-2*d^4*log(im+c*x))
@test integrate((d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-16//5*b*c^-1*d^4*log(1+-1*im*c*x)+-8//5*im*b*x*d^4+-2//5*b*c^-1*d^4*(1+im*c*x)^2+-2//15*b*c^-1*d^4*(1+im*c*x)^3+-1//20*b*c^-1*d^4*(1+im*c*x)^4+-1//5*im*c^-1*d^4*(1+im*c*x)^5*(a+b*arctan(c*x)))
@test integrate(x^-1*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(a*d^4*log(x)+-13//4*b*d^4*arctan(c*x)+(1/2)*im*b*d^4*Polylogarithms.polylog(2,-1*im*c*x)+-3*c^2*d^4*x^2*(a+b*arctan(c*x))+-8//3*im*b*d^4*log(1+c^2*x^2)+-1//2*im*b*d^4*Polylogarithms.polylog(2,im*c*x)+-1//12*b*c^3*d^4*x^3+1//4*c^4*d^4*x^4*(a+b*arctan(c*x))+13//4*b*c*x*d^4+4*im*a*c*x*d^4+-4//3*im*c^3*d^4*x^3*(a+b*arctan(c*x))+2//3*im*b*c^2*d^4*x^2+4*im*b*c*x*d^4*arctan(c*x))
@test integrate(x^-2*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-1*d^4*x^-1*(a+b*arctan(c*x))+b*c*d^4*log(x)+-6*a*x*c^2*d^4+-2*b*c*d^4*Polylogarithms.polylog(2,-1*im*c*x)+2*b*c*d^4*Polylogarithms.polylog(2,im*c*x)+-1//6*b*c^3*d^4*x^2+1//3*c^4*d^4*x^3*(a+b*arctan(c*x))+8//3*b*c*d^4*log(1+c^2*x^2)+-6*b*x*c^2*d^4*arctan(c*x)+-2*im*b*c*d^4*arctan(c*x)+-2*im*c^3*d^4*x^2*(a+b*arctan(c*x))+2*im*b*x*c^2*d^4+4*im*a*c*d^4*log(x))
@test integrate(x^-3*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-1//2*d^4*x^-2*(a+b*arctan(c*x))+(1/2)*c^4*d^4*x^2*(a+b*arctan(c*x))+-6*a*c^2*d^4*log(x)+-1//2*b*c*d^4*x^-1+-1//2*b*x*c^3*d^4+-4*im*a*x*c^3*d^4+-4*im*c*d^4*x^-1*(a+b*arctan(c*x))+-3*im*b*c^2*d^4*Polylogarithms.polylog(2,-1*im*c*x)+3*im*b*c^2*d^4*Polylogarithms.polylog(2,im*c*x)+4*im*b*c^2*d^4*log(x)+-4*im*b*x*c^3*d^4*arctan(c*x))
@test integrate(x^-4*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-1//3*d^4*x^-3*(a+b*arctan(c*x))+a*x*c^4*d^4+-2*b*c^3*d^4*Polylogarithms.polylog(2,im*c*x)+2*b*c^3*d^4*Polylogarithms.polylog(2,-1*im*c*x)+6*c^2*d^4*x^-1*(a+b*arctan(c*x))+-19//3*b*c^3*d^4*log(x)+-1//6*b*c*d^4*x^-2+8//3*b*c^3*d^4*log(1+c^2*x^2)+b*x*c^4*d^4*arctan(c*x)+-4*im*a*c^3*d^4*log(x)+-2*im*b*c^2*d^4*x^-1+-2*im*b*c^3*d^4*arctan(c*x)+-2*im*c*d^4*x^-2*(a+b*arctan(c*x)))
@test integrate(x^-5*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-1//4*d^4*x^-4*(a+b*arctan(c*x))+a*c^4*d^4*log(x)+3*c^2*d^4*x^-2*(a+b*arctan(c*x))+-1//12*b*c*d^4*x^-3+13//4*b*c^3*d^4*x^-1+13//4*b*c^4*d^4*arctan(c*x)+(1/2)*im*b*c^4*d^4*Polylogarithms.polylog(2,-1*im*c*x)+4*im*c^3*d^4*x^-1*(a+b*arctan(c*x))+-16//3*im*b*c^4*d^4*log(x)+-4//3*im*c*d^4*x^-3*(a+b*arctan(c*x))+-2//3*im*b*c^2*d^4*x^-2+-1//2*im*b*c^4*d^4*Polylogarithms.polylog(2,im*c*x)+8//3*im*b*c^4*d^4*log(1+c^2*x^2))
@test integrate(x^-6*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-16//5*b*c^5*d^4*log(im+c*x)+-1//5*d^4*x^-5*(1+im*c*x)^5*(a+b*arctan(c*x))+-1//20*b*c*d^4*x^-4+11//10*b*c^3*d^4*x^-2+16//5*b*c^5*d^4*log(x)+3*im*b*c^4*d^4*x^-1+-1//3*im*b*c^2*d^4*x^-3)
@test integrate(x^-7*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-13//6*b*c^5*d^4*x^-1+-1//6*d^4*x^-6*(1+im*c*x)^5*(a+b*arctan(c*x))+-1//30*b*c*d^4*x^-5+5//9*b*c^3*d^4*x^-3+-32//15*im*b*c^6*d^4*log(im+c*x)+-1//5*im*b*c^2*d^4*x^-4+16//15*im*b*c^4*d^4*x^-2+32//15*im*b*c^6*d^4*log(x)+1//30*im*c*d^4*x^-5*(1+im*c*x)^5*(a+b*arctan(c*x)))
@test integrate(x^-8*(d+im*c*d*x)^4*(a+b*arctan(c*x)), x) == :(-1//7*d^4*x^-7*(a+b*arctan(c*x))+-176//105*b*c^7*d^4*log(x)+-88//105*b*c^5*d^4*x^-2+-1//3*c^4*d^4*x^-3*(a+b*arctan(c*x))+-1//42*b*c*d^4*x^-6+1//210*b*c^7*d^4*log(im+-1*c*x)+6//5*c^2*d^4*x^-5*(a+b*arctan(c*x))+47//140*b*c^3*d^4*x^-4+117//70*b*c^7*d^4*log(im+c*x)+im*c^3*d^4*x^-4*(a+b*arctan(c*x))+-5//3*im*b*c^6*d^4*x^-1+-2//3*im*c*d^4*x^-6*(a+b*arctan(c*x))+-2//15*im*b*c^2*d^4*x^-5+5//9*im*b*c^4*d^4*x^-3)
@test integrate(x^3*(d+im*c*d*x)^-1*(a+b*arctan(c*x)), x) == :(c^-4*d^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+(1/2)*b*c^-4*d^-1*arctan(c*x)+(1/2)*c^-2*d^-1*x^2*(a+b*arctan(c*x))+-1//2*b*x*c^-3*d^-1+im*a*x*c^-3*d^-1+(1/2)*im*b*c^-4*d^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-2//3*im*b*c^-4*d^-1*log(1+c^2*x^2)+-1//3*im*c^-1*d^-1*x^3*(a+b*arctan(c*x))+1//6*im*b*c^-2*d^-1*x^2+im*b*x*c^-3*d^-1*arctan(c*x))
@test integrate(x^2*(d+im*c*d*x)^-1*(a+b*arctan(c*x)), x) == :(a*x*c^-2*d^-1+(1/2)*b*c^-3*d^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//2*b*c^-3*d^-1*log(1+c^2*x^2)+b*x*c^-2*d^-1*arctan(c*x)+(1/2)*im*b*x*c^-2*d^-1+-1*im*c^-3*d^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//2*im*b*c^-3*d^-1*arctan(c*x)+-1//2*im*c^-1*d^-1*x^2*(a+b*arctan(c*x)))
@test integrate(x*(d+im*c*d*x)^-1*(a+b*arctan(c*x)), x) == :(-1*c^-2*d^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+(1/2)*im*b*c^-2*d^-1*log(1+c^2*x^2)+-1*im*a*x*c^-1*d^-1+-1//2*im*b*c^-2*d^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*b*x*c^-1*d^-1*arctan(c*x))
@test integrate((d+im*c*d*x)^-1*(a+b*arctan(c*x)), x) == :(-1//2*b*c^-1*d^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+im*c^-1*d^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^-1*(d+im*c*d*x)^-1*(a+b*arctan(c*x)), x) == :(d^-1*(a+b*arctan(c*x))*log(2+-2*(1+im*c*x)^-1)+(1/2)*im*b*d^-1*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1))
@test integrate(x^-2*(d+im*c*d*x)^-1*(a+b*arctan(c*x)), x) == :(-1*d^-1*x^-1*(a+b*arctan(c*x))+b*c*d^-1*log(x)+(1/2)*b*c*d^-1*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-1//2*b*c*d^-1*log(1+c^2*x^2)+-1*im*c*d^-1*(a+b*arctan(c*x))*log(2+-2*(1+im*c*x)^-1))
@test integrate(x^-3*(d+im*c*d*x)^-1*(a+b*arctan(c*x)), x) == :(-1//2*d^-1*x^-2*(a+b*arctan(c*x))+-1*c^2*d^-1*(a+b*arctan(c*x))*log(2+-2*(1+im*c*x)^-1)+-1//2*b*c*d^-1*x^-1+-1//2*b*c^2*d^-1*arctan(c*x)+im*c*d^-1*x^-1*(a+b*arctan(c*x))+(1/2)*im*b*c^2*d^-1*log(1+c^2*x^2)+-1*im*b*c^2*d^-1*log(x)+-1//2*im*b*c^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1))
@test integrate(x^-4*(d+im*c*d*x)^-1*(a+b*arctan(c*x)), x) == :(-1//3*d^-1*x^-3*(a+b*arctan(c*x))+c^2*d^-1*x^-1*(a+b*arctan(c*x))+-4//3*b*c^3*d^-1*log(x)+-1//2*b*c^3*d^-1*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-1//6*b*c*d^-1*x^-2+2//3*b*c^3*d^-1*log(1+c^2*x^2)+im*c^3*d^-1*(a+b*arctan(c*x))*log(2+-2*(1+im*c*x)^-1)+(1/2)*im*b*c^2*d^-1*x^-1+(1/2)*im*b*c^3*d^-1*arctan(c*x)+(1/2)*im*c*d^-1*x^-2*(a+b*arctan(c*x)))
@test integrate(x^3*(d+im*c*d*x)^-2*(a+b*arctan(c*x)), x) == :((1/2)*b*x*c^-3*d^-2+(1/2)*b*c^-4*d^-2*(im+-1*c*x)^-1+-1*b*c^-4*d^-2*arctan(c*x)+-1*c^-4*d^-2*(3a+3*b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//2*c^-2*d^-2*x^2*(a+b*arctan(c*x))+im*b*c^-4*d^-2*log(1+c^2*x^2)+im*c^-4*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+-2*im*a*x*c^-3*d^-2+-3//2*im*b*c^-4*d^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-2*im*b*x*c^-3*d^-2*arctan(c*x))
@test integrate(x^2*(d+im*c*d*x)^-2*(a+b*arctan(c*x)), x) == :(c^-3*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+(1/2)*b*c^-3*d^-2*log(1+c^2*x^2)+-1*a*x*c^-2*d^-2+-1*b*c^-3*d^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+(1/2)*im*b*c^-3*d^-2*arctan(c*x)+-1*b*x*c^-2*d^-2*arctan(c*x)+2*im*c^-3*d^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//2*im*b*c^-3*d^-2*(im+-1*c*x)^-1)
@test integrate(x*(d+im*c*d*x)^-2*(a+b*arctan(c*x)), x) == :(c^-2*d^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+(1/2)*b*c^-2*d^-2*arctan(c*x)+-1//2*b*c^-2*d^-2*(im+-1*c*x)^-1+(1/2)*im*b*c^-2*d^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*c^-2*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x)))
@test integrate((d+im*c*d*x)^-2*(a+b*arctan(c*x)), x) == :(im*c^-1*d^-2*(1+im*c*x)^-1*(a+b*arctan(c*x))+(1/2)*im*b*c^-1*d^-2*(im+-1*c*x)^-1+-1//2*im*b*c^-1*d^-2*arctan(c*x))
@test integrate(x^-1*(d+im*c*d*x)^-2*(a+b*arctan(c*x)), x) == :(a*d^-2*log(x)+d^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+(1/2)*b*d^-2*(im+-1*c*x)^-1+-1//2*b*d^-2*arctan(c*x)+im*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+(1/2)*im*b*d^-2*Polylogarithms.polylog(2,-1*im*c*x)+(1/2)*im*b*d^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//2*im*b*d^-2*Polylogarithms.polylog(2,im*c*x))
@test integrate(x^-2*(d+im*c*d*x)^-2*(a+b*arctan(c*x)), x) == :(-1*d^-2*x^-1*(a+b*arctan(c*x))+b*c*d^-2*Polylogarithms.polylog(2,-1*im*c*x)+b*c*d^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+b*c*d^-2*log(x)+c*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+-1*b*c*d^-2*Polylogarithms.polylog(2,im*c*x)+-1//2*b*c*d^-2*log(1+c^2*x^2)+(1/2)*im*b*c*d^-2*arctan(c*x)+-2*im*a*c*d^-2*log(x)+-2*im*c*d^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//2*im*b*c*d^-2*(im+-1*c*x)^-1)
@test integrate(x^-3*(d+im*c*d*x)^-2*(a+b*arctan(c*x)), x) == :(-1//2*d^-2*x^-2*(a+b*arctan(c*x))+-3*a*c^2*d^-2*log(x)+-3*c^2*d^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//2*b*c*d^-2*x^-1+-1//2*b*c^2*d^-2*(im+-1*c*x)^-1+im*b*c^2*d^-2*log(1+c^2*x^2)+-1*im*c^2*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+-2*im*b*c^2*d^-2*log(x)+2*im*c*d^-2*x^-1*(a+b*arctan(c*x))+-3//2*im*b*c^2*d^-2*Polylogarithms.polylog(2,-1*im*c*x)+-3//2*im*b*c^2*d^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3//2*im*b*c^2*d^-2*Polylogarithms.polylog(2,im*c*x))
@test integrate(x^4*(d+im*c*d*x)^-3*(a+b*arctan(c*x)), x) == :(c^-5*d^-3*(im+-1*c*x)^-1*(4a+4*b*arctan(c*x))+-3*a*x*c^-4*d^-3+-3*b*c^-5*d^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//8*b*c^-5*d^-3*(im+-1*c*x)^-2+3//2*b*c^-5*d^-3*log(1+c^2*x^2)+(1/2)*im*c^-3*d^-3*x^2*(a+b*arctan(c*x))+-3*b*x*c^-4*d^-3*arctan(c*x)+6*im*c^-5*d^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-15//8*im*b*c^-5*d^-3*(im+-1*c*x)^-1+-1//2*im*b*x*c^-4*d^-3+-1//2*im*c^-5*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+19//8*im*b*c^-5*d^-3*arctan(c*x))
@test integrate(x^3*(d+im*c*d*x)^-3*(a+b*arctan(c*x)), x) == :(c^-4*d^-3*(3a+3*b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-11//8*b*c^-4*d^-3*(im+-1*c*x)^-1+-1//2*c^-4*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+11//8*b*c^-4*d^-3*arctan(c*x)+im*a*x*c^-3*d^-3+-3*im*c^-4*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))+-1//2*im*b*c^-4*d^-3*log(1+c^2*x^2)+1//8*im*b*c^-4*d^-3*(im+-1*c*x)^-2+3//2*im*b*c^-4*d^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+im*b*x*c^-3*d^-3*arctan(c*x))
@test integrate(x^2*(d+im*c*d*x)^-3*(a+b*arctan(c*x)), x) == :((1/2)*b*c^-3*d^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*c^-3*d^-3*(im+-1*c*x)^-1*(2a+2*b*arctan(c*x))+1//8*b*c^-3*d^-3*(im+-1*c*x)^-2+(1/2)*im*c^-3*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+-1*im*c^-3*d^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-7//8*im*b*c^-3*d^-3*arctan(c*x)+7//8*im*b*c^-3*d^-3*(im+-1*c*x)^-1)
@test integrate(x*(d+im*c*d*x)^-3*(a+b*arctan(c*x)), x) == :((1/2)*d^-3*x^2*(1+im*c*x)^-2*(a+b*arctan(c*x))+1//8*b*c^-2*d^-3*arctan(c*x)+3//8*b*c^-2*d^-3*(im+-1*c*x)^-1+-1//8*im*b*c^-2*d^-3*(im+-1*c*x)^-2)
@test integrate((d+im*c*d*x)^-3*(a+b*arctan(c*x)), x) == :(-1//8*b*c^-1*d^-3*(im+-1*c*x)^-2+(1/2)*im*c^-1*d^-3*(1+im*c*x)^-2*(a+b*arctan(c*x))+-1//8*im*b*c^-1*d^-3*arctan(c*x)+1//8*im*b*c^-1*d^-3*(im+-1*c*x)^-1)
@test integrate(x^-1*(d+im*c*d*x)^-3*(a+b*arctan(c*x)), x) == :(a*d^-3*log(x)+d^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-5//8*b*d^-3*arctan(c*x)+-1//2*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+5//8*b*d^-3*(im+-1*c*x)^-1+im*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))+(1/2)*im*b*d^-3*Polylogarithms.polylog(2,-1*im*c*x)+(1/2)*im*b*d^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//2*im*b*d^-3*Polylogarithms.polylog(2,im*c*x)+1//8*im*b*d^-3*(im+-1*c*x)^-2)
@test integrate(x^-2*(d+im*c*d*x)^-3*(a+b*arctan(c*x)), x) == :(-1*d^-3*x^-1*(a+b*arctan(c*x))+b*c*d^-3*log(x)+2*c*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))+-3//2*b*c*d^-3*Polylogarithms.polylog(2,im*c*x)+-1//2*b*c*d^-3*log(1+c^2*x^2)+1//8*b*c*d^-3*(im+-1*c*x)^-2+3//2*b*c*d^-3*Polylogarithms.polylog(2,-1*im*c*x)+3//2*b*c*d^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+(1/2)*im*c*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+-3*im*a*c*d^-3*log(x)+-3*im*c*d^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-9//8*im*b*c*d^-3*(im+-1*c*x)^-1+9//8*im*b*c*d^-3*arctan(c*x))
@test integrate(x^-3*(d+im*c*d*x)^-3*(a+b*arctan(c*x)), x) == :(-1//2*d^-3*x^-2*(a+b*arctan(c*x))+(1/2)*c^2*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+-6*a*c^2*d^-3*log(x)+-6*c^2*d^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-13//8*b*c^2*d^-3*(im+-1*c*x)^-1+-1//2*b*c*d^-3*x^-1+9//8*b*c^2*d^-3*arctan(c*x)+-3*im*b*c^2*d^-3*Polylogarithms.polylog(2,-1*im*c*x)+-3*im*b*c^2*d^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-3*im*b*c^2*d^-3*log(x)+-3*im*c^2*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))+3*im*b*c^2*d^-3*Polylogarithms.polylog(2,im*c*x)+3*im*c*d^-3*x^-1*(a+b*arctan(c*x))+-1//8*im*b*c^2*d^-3*(im+-1*c*x)^-2+3//2*im*b*c^2*d^-3*log(1+c^2*x^2))
@test integrate((1+im*c*x)^-4*(a+b*arctan(c*x)), x) == :(-1//24*b*c^-1*(im+-1*c*x)^-2+-1//18*im*b*c^-1*(im+-1*c*x)^-3+-1//24*im*b*c^-1*arctan(c*x)+1//3*im*c^-1*(1+im*c*x)^-3*(a+b*arctan(c*x))+1//24*im*b*c^-1*(im+-1*c*x)^-1)
@test integrate((c*x+im*a*c*x^2)^-1*arctan(a*x), x) == :(c^-1*arctan(a*x)*log(2+-2*(1+im*a*x)^-1)+(1/2)*im*c^-1*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+im*c*d*x), x) == :(-9//20*d*c^-4*(a+b*arctan(c*x))^2+1//4*d*x^4*(a+b*arctan(c*x))^2+-1//3*d*b^2*c^-4*log(1+c^2*x^2)+-1//5*d*b^2*c^-4*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+1//12*d*b^2*c^-2*x^2+(1/2)*a*b*d*x*c^-3+(1/2)*d*x*b^2*c^-3*arctan(c*x)+-3//10*im*d*x*b^2*c^-3+-1//6*b*d*c^-1*x^3*(a+b*arctan(c*x))+-1//10*im*b*d*x^4*(a+b*arctan(c*x))+1//5*im*c*d*x^5*(a+b*arctan(c*x))^2+1//30*im*d*b^2*c^-1*x^3+3//10*im*d*b^2*c^-4*arctan(c*x)+1//5*im*b*d*c^-2*x^2*(a+b*arctan(c*x))+2//5*im*b*d*c^-4*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+im*c*d*x), x) == :(1//3*d*x^3*(a+b*arctan(c*x))^2+-7//12*im*d*c^-3*(a+b*arctan(c*x))^2+-1//3*d*b^2*c^-3*arctan(c*x)+1//3*d*x*b^2*c^-2+-2//3*b*d*c^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//3*im*d*b^2*c^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//3*im*d*b^2*c^-3*log(1+c^2*x^2)+-1//3*b*d*c^-1*x^2*(a+b*arctan(c*x))+-1//6*im*b*d*x^3*(a+b*arctan(c*x))+1//4*im*c*d*x^4*(a+b*arctan(c*x))^2+1//12*im*d*b^2*c^-1*x^2+(1/2)*im*a*b*d*x*c^-2+(1/2)*im*d*x*b^2*c^-2*arctan(c*x))
@test integrate(x*(a+b*arctan(c*x))^2*(d+im*c*d*x), x) == :((1/2)*d*x^2*(a+b*arctan(c*x))^2+5//6*d*c^-2*(a+b*arctan(c*x))^2+(1/2)*d*b^2*c^-2*log(1+c^2*x^2)+1//3*d*b^2*c^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*a*b*d*x*c^-1+-1*d*x*b^2*c^-1*arctan(c*x)+-1//3*im*b*d*x^2*(a+b*arctan(c*x))+-1//3*im*d*b^2*c^-2*arctan(c*x)+1//3*im*c*d*x^3*(a+b*arctan(c*x))^2+1//3*im*d*x*b^2*c^-1+-2//3*im*b*d*c^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate((a+b*arctan(c*x))^2*(d+im*c*d*x), x) == :((1/2)*im*d*b^2*c^-1*log(1+c^2*x^2)+-1*im*a*b*d*x+-1*im*d*x*b^2*arctan(c*x)+-1*im*d*b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+2*b*d*c^-1*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1//2*im*d*c^-1*(1+im*c*x)^2*(a+b*arctan(c*x))^2)
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+im*c*d*x), x) == :(-1*d*(a+b*arctan(c*x))^2+(1/2)*d*b^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1*d*b^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*d*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*d*b^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+im*b*d*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+im*c*d*x*(a+b*arctan(c*x))^2+-1*im*b*d*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*im*b*d*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+im*c*d*x), x) == :(-1*d*x^-1*(a+b*arctan(c*x))^2+-1*im*c*d*(a+b*arctan(c*x))^2+b*c*d*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+(1/2)*im*c*d*b^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1*im*c*d*b^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-1*b*c*d*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+2*im*c*d*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+2*b*c*d*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-1//2*im*c*d*b^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+im*c*d*x), x) == :((1/2)*d*c^2*(a+b*arctan(c*x))^2+-1//2*d*x^-2*(a+b*arctan(c*x))^2+d*b^2*c^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+d*b^2*c^2*log(x)+-1//2*d*b^2*c^2*log(1+c^2*x^2)+-1*im*c*d*x^-1*(a+b*arctan(c*x))^2+-1*b*c*d*x^-1*(a+b*arctan(c*x))+2*im*b*d*c^2*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1))
@test integrate(x^-4*(a+b*arctan(c*x))^2*(d+im*c*d*x), x) == :(-1//3*d*x^-3*(a+b*arctan(c*x))^2+-1//3*d*b^2*c^2*x^-1+-1//3*d*b^2*c^3*arctan(c*x)+-1//6*im*d*c^3*(a+b*arctan(c*x))^2+im*d*b^2*c^3*log(x)+-2//3*b*d*c^3*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-1//2*im*c*d*x^-2*(a+b*arctan(c*x))^2+-1//2*im*d*b^2*c^3*log(1+c^2*x^2)+-1//3*b*c*d*x^-2*(a+b*arctan(c*x))+1//3*im*d*b^2*c^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-1*im*b*d*c^2*x^-1*(a+b*arctan(c*x)))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+im*c*d*x)^2, x) == :(-49//60*c^-4*d^2*(a+b*arctan(c*x))^2+-1//60*b^2*d^2*x^4+1//4*d^2*x^4*(a+b*arctan(c*x))^2+-53//90*b^2*c^-4*d^2*log(1+c^2*x^2)+-2//5*b^2*c^-4*d^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//6*c^2*d^2*x^6*(a+b*arctan(c*x))^2+31//180*b^2*c^-2*d^2*x^2+-5//18*b*c^-1*d^2*x^3*(a+b*arctan(c*x))+-3//5*im*x*b^2*c^-3*d^2+-1//5*im*b*d^2*x^4*(a+b*arctan(c*x))+1//15*im*b^2*c^-1*d^2*x^3+1//15*b*c*d^2*x^5*(a+b*arctan(c*x))+2//5*im*c*d^2*x^5*(a+b*arctan(c*x))^2+3//5*im*b^2*c^-4*d^2*arctan(c*x)+5//6*a*b*x*c^-3*d^2+5//6*x*b^2*c^-3*d^2*arctan(c*x)+2//5*im*b*c^-2*d^2*x^2*(a+b*arctan(c*x))+4//5*im*b*c^-4*d^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^2, x) == :(-1//30*b^2*d^2*x^3+1//3*d^2*x^3*(a+b*arctan(c*x))^2+-31//30*im*c^-3*d^2*(a+b*arctan(c*x))^2+-19//30*b^2*c^-3*d^2*arctan(c*x)+-1//5*c^2*d^2*x^5*(a+b*arctan(c*x))^2+19//30*x*b^2*c^-2*d^2+(1/2)*im*c*d^2*x^4*(a+b*arctan(c*x))^2+-16//15*b*c^-3*d^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-8//15*im*b^2*c^-3*d^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-8//15*b*c^-1*d^2*x^2*(a+b*arctan(c*x))+-2//3*im*b^2*c^-3*d^2*log(1+c^2*x^2)+-1//3*im*b*d^2*x^3*(a+b*arctan(c*x))+1//6*im*b^2*c^-1*d^2*x^2+1//10*b*c*d^2*x^4*(a+b*arctan(c*x))+im*a*b*x*c^-2*d^2+im*x*b^2*c^-2*d^2*arctan(c*x))
@test integrate(x*(a+b*arctan(c*x))^2*(d+im*c*d*x)^2, x) == :((1/2)*d^2*x^2*(a+b*arctan(c*x))^2+-1//12*b^2*d^2*x^2+17//12*c^-2*d^2*(a+b*arctan(c*x))^2+-1//4*c^2*d^2*x^4*(a+b*arctan(c*x))^2+2//3*b^2*c^-2*d^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+5//6*b^2*c^-2*d^2*log(1+c^2*x^2)+-3//2*a*b*x*c^-1*d^2+-3//2*x*b^2*c^-1*d^2*arctan(c*x)+-2//3*im*b*d^2*x^2*(a+b*arctan(c*x))+-2//3*im*b^2*c^-2*d^2*arctan(c*x)+1//6*b*c*d^2*x^3*(a+b*arctan(c*x))+2//3*im*c*d^2*x^3*(a+b*arctan(c*x))^2+2//3*im*x*b^2*c^-1*d^2+-4//3*im*b*c^-2*d^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate((a+b*arctan(c*x))^2*(d+im*c*d*x)^2, x) == :(-1//3*x*b^2*d^2+1//3*b^2*c^-1*d^2*arctan(c*x)+im*b^2*c^-1*d^2*log(1+c^2*x^2)+-2*im*a*b*x*d^2+-2*im*x*b^2*d^2*arctan(c*x)+-4//3*im*b^2*c^-1*d^2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//3*im*c^-1*d^2*(1+im*c*x)^3*(a+b*arctan(c*x))^2+1//3*b*c*d^2*x^2*(a+b*arctan(c*x))+8//3*b*c^-1*d^2*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+im*c*d*x)^2, x) == :(-5//2*d^2*(a+b*arctan(c*x))^2+(1/2)*b^2*d^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-2*b^2*d^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*d^2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*b^2*d^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//2*b^2*d^2*log(1+c^2*x^2)+-1//2*c^2*d^2*x^2*(a+b*arctan(c*x))^2+im*b*d^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+a*b*c*x*d^2+c*x*b^2*d^2*arctan(c*x)+-1*im*b*d^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*im*c*x*d^2*(a+b*arctan(c*x))^2+4*im*b*d^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^2, x) == :(-1*d^2*x^-1*(a+b*arctan(c*x))^2+-1*x*c^2*d^2*(a+b*arctan(c*x))^2+-2*im*c*d^2*(a+b*arctan(c*x))^2+im*c*b^2*d^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1*im*c*b^2*d^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*c*b^2*d^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-1*im*c*b^2*d^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-2*b*c*d^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-2*b*c*d^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+2*b*c*d^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*b*c*d^2*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+4*im*c*d^2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+im*c*d*x)^2, x) == :(-1//2*d^2*x^-2*(a+b*arctan(c*x))^2+3//2*c^2*d^2*(a+b*arctan(c*x))^2+b^2*c^2*d^2*log(x)+(1/2)*b^2*c^2*d^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-2*c^2*d^2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+2*b^2*c^2*d^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-1//2*b^2*c^2*d^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1//2*b^2*c^2*d^2*log(1+c^2*x^2)+-1*b*c*d^2*x^-1*(a+b*arctan(c*x))+-2*im*c*d^2*x^-1*(a+b*arctan(c*x))^2+im*b*c^2*d^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*b*c^2*d^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+4*im*b*c^2*d^2*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1))
@test integrate(x^-4*(a+b*arctan(c*x))^2*(d+im*c*d*x)^2, x) == :(-1//3*b^2*c^2*d^2*x^-1+-1//3*b^2*c^3*d^2*arctan(c*x)+-1//3*d^2*x^-3*(1+im*c*x)^3*(a+b*arctan(c*x))^2+-1*im*b^2*c^3*d^2*log(1+c^2*x^2)+2*im*b^2*c^3*d^2*log(x)+-8//3*a*b*c^3*d^2*log(x)+-8//3*b*c^3*d^2*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-4//3*im*b^2*c^3*d^2*Polylogarithms.polylog(2,-1*im*c*x)+-1//3*b*c*d^2*x^-2*(a+b*arctan(c*x))+4//3*im*b^2*c^3*d^2*Polylogarithms.polylog(2,im*c*x)+4//3*im*b^2*c^3*d^2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-2*im*b*c^2*d^2*x^-1*(a+b*arctan(c*x)))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-209//140*c^-4*d^3*(a+b*arctan(c*x))^2+-1//20*b^2*d^3*x^4+1//4*d^3*x^4*(a+b*arctan(c*x))^2+-26//35*b^2*c^-4*d^3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-11//10*b^2*c^-4*d^3*log(1+c^2*x^2)+-1//2*c^2*d^3*x^6*(a+b*arctan(c*x))^2+7//20*b^2*c^-2*d^3*x^2+-122//105*im*x*b^2*c^-3*d^3+-13//35*im*b*d^3*x^4*(a+b*arctan(c*x))+-1//2*b*c^-1*d^3*x^3*(a+b*arctan(c*x))+-1//7*im*c^3*d^3*x^7*(a+b*arctan(c*x))^2+-1//105*im*c*b^2*d^3*x^5+1//5*b*c*d^3*x^5*(a+b*arctan(c*x))+3//2*a*b*x*c^-3*d^3+3//2*x*b^2*c^-3*d^3*arctan(c*x)+3//5*im*c*d^3*x^5*(a+b*arctan(c*x))^2+44//315*im*b^2*c^-1*d^3*x^3+122//105*im*b^2*c^-4*d^3*arctan(c*x)+1//21*im*b*c^2*d^3*x^6*(a+b*arctan(c*x))+26//35*im*b*c^-2*d^3*x^2*(a+b*arctan(c*x))+52//35*im*b*c^-4*d^3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-1//10*b^2*d^3*x^3+1//3*d^3*x^3*(a+b*arctan(c*x))^2+-37//20*im*c^-3*d^3*(a+b*arctan(c*x))^2+-37//30*b^2*c^-3*d^3*arctan(c*x)+-3//5*c^2*d^3*x^5*(a+b*arctan(c*x))^2+37//30*x*b^2*c^-2*d^3+-113//90*im*b^2*c^-3*d^3*log(1+c^2*x^2)+-28//15*b*c^-3*d^3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-14//15*im*b^2*c^-3*d^3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-14//15*b*c^-1*d^3*x^2*(a+b*arctan(c*x))+-11//18*im*b*d^3*x^3*(a+b*arctan(c*x))+-1//6*im*c^3*d^3*x^6*(a+b*arctan(c*x))^2+-1//60*im*c*b^2*d^3*x^4+3//4*im*c*d^3*x^4*(a+b*arctan(c*x))^2+3//10*b*c*d^3*x^4*(a+b*arctan(c*x))+61//180*im*b^2*c^-1*d^3*x^2+1//15*im*b*c^2*d^3*x^5*(a+b*arctan(c*x))+11//6*im*a*b*x*c^-2*d^3+11//6*im*x*b^2*c^-2*d^3*arctan(c*x))
@test integrate(x*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-1//4*b^2*d^3*x^2+-6//5*b^2*c^-2*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//5*c^-2*d^3*(1+im*c*x)^5*(a+b*arctan(c*x))^2+1//4*c^-2*d^3*(1+im*c*x)^4*(a+b*arctan(c*x))^2+3//2*b^2*c^-2*d^3*log(1+c^2*x^2)+(1/2)*b*c*d^3*x^3*(a+b*arctan(c*x))+-13//10*im*b^2*c^-2*d^3*arctan(c*x)+-6//5*im*b*d^3*x^2*(a+b*arctan(c*x))+-5//2*a*b*x*c^-1*d^3+-5//2*x*b^2*c^-1*d^3*arctan(c*x)+-1//30*im*c*b^2*d^3*x^3+13//10*im*x*b^2*c^-1*d^3+-12//5*im*b*c^-2*d^3*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+1//10*im*b*c^2*d^3*x^4*(a+b*arctan(c*x)))
@test integrate((a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-1*x*b^2*d^3+b^2*c^-1*d^3*arctan(c*x)+b*c*d^3*x^2*(a+b*arctan(c*x))+-2*im*b^2*c^-1*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+4*b*c^-1*d^3*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-7//2*im*a*b*x*d^3+-7//2*im*x*b^2*d^3*arctan(c*x)+-1//4*im*c^-1*d^3*(1+im*c*x)^4*(a+b*arctan(c*x))^2+-1//12*im*c*b^2*d^3*x^2+11//6*im*b^2*c^-1*d^3*log(1+c^2*x^2)+1//6*im*b*c^2*d^3*x^3*(a+b*arctan(c*x)))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-29//6*d^3*(a+b*arctan(c*x))^2+(1/2)*b^2*d^3*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+2*d^3*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-10//3*b^2*d^3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-3//2*b^2*d^3*log(1+c^2*x^2)+-1//2*b^2*d^3*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-3//2*c^2*d^3*x^2*(a+b*arctan(c*x))^2+1//3*im*b^2*d^3*arctan(c*x)+im*b*d^3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-1*im*b*d^3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3*im*c*x*d^3*(a+b*arctan(c*x))^2+3*a*b*c*x*d^3+3*c*x*b^2*d^3*arctan(c*x)+-1//3*im*c*x*b^2*d^3+-1//3*im*c^3*d^3*x^3*(a+b*arctan(c*x))^2+20//3*im*b*d^3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+1//3*im*b*c^2*d^3*x^2*(a+b*arctan(c*x)))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-1*d^3*x^-1*(a+b*arctan(c*x))^2+-3*x*c^2*d^3*(a+b*arctan(c*x))^2+-9//2*im*c*d^3*(a+b*arctan(c*x))^2+-1*im*c*b^2*d^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-6*b*c*d^3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-3*im*c*b^2*d^3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-3*b*c*d^3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+2*b*c*d^3*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+3*b*c*d^3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+6*im*c*d^3*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-3//2*im*c*b^2*d^3*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//2*im*c*b^2*d^3*log(1+c^2*x^2)+-1//2*im*c^3*d^3*x^2*(a+b*arctan(c*x))^2+3//2*im*c*b^2*d^3*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+im*a*b*x*c^2*d^3+im*x*b^2*c^2*d^3*arctan(c*x))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-1//2*d^3*x^-2*(a+b*arctan(c*x))^2+7//2*c^2*d^3*(a+b*arctan(c*x))^2+b^2*c^2*d^3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+b^2*c^2*d^3*log(x)+-6*c^2*d^3*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+3*b^2*c^2*d^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-3//2*b^2*c^2*d^3*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1//2*b^2*c^2*d^3*log(1+c^2*x^2)+3//2*b^2*c^2*d^3*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1*im*x*c^3*d^3*(a+b*arctan(c*x))^2+-1*b*c*d^3*x^-1*(a+b*arctan(c*x))+-3*im*c*d^3*x^-1*(a+b*arctan(c*x))^2+-3*im*b*c^2*d^3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-2*im*b*c^2*d^3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+3*im*b*c^2*d^3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+6*im*b*c^2*d^3*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1))
@test integrate(x^-4*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-1//3*d^3*x^-3*(a+b*arctan(c*x))^2+3*c^2*d^3*x^-1*(a+b*arctan(c*x))^2+-1//3*b^2*c^2*d^3*x^-1+-1//3*b^2*c^3*d^3*arctan(c*x)+11//6*im*c^3*d^3*(a+b*arctan(c*x))^2+b*c^3*d^3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+(1/2)*im*b^2*c^3*d^3*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1*b*c^3*d^3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-2*im*c^3*d^3*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+3*im*b^2*c^3*d^3*log(x)+-20//3*b*c^3*d^3*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-3//2*im*c*d^3*x^-2*(a+b*arctan(c*x))^2+-3//2*im*b^2*c^3*d^3*log(1+c^2*x^2)+-1//2*im*b^2*c^3*d^3*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1//3*b*c*d^3*x^-2*(a+b*arctan(c*x))+10//3*im*b^2*c^3*d^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-3*im*b*c^2*d^3*x^-1*(a+b*arctan(c*x)))
@test integrate(x^-5*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-2*b^2*c^4*d^3*Polylogarithms.polylog(2,im*c*x)+-2*b^2*c^4*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+2*b^2*c^4*d^3*Polylogarithms.polylog(2,-1*im*c*x)+-11//3*b^2*c^4*d^3*log(x)+-1//4*d^3*x^-4*(1+im*c*x)^4*(a+b*arctan(c*x))^2+-1//12*b^2*c^2*d^3*x^-2+11//6*b^2*c^4*d^3*log(1+c^2*x^2)+-1*im*b^2*c^3*d^3*x^-1+-1*im*b^2*c^4*d^3*arctan(c*x)+-1//6*b*c*d^3*x^-3*(a+b*arctan(c*x))+7//2*b*c^3*d^3*x^-1*(a+b*arctan(c*x))+-1*im*b*c^2*d^3*x^-2*(a+b*arctan(c*x))+-4*im*a*b*c^4*d^3*log(x)+-4*im*b*c^4*d^3*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1))
@test integrate(x^-6*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-1//5*d^3*x^-5*(1+im*c*x)^4*(a+b*arctan(c*x))^2+-1//30*b^2*c^2*d^3*x^-3+13//10*b^2*c^4*d^3*x^-1+13//10*b^2*c^5*d^3*arctan(c*x)+-3*im*b^2*c^5*d^3*log(x)+-6//5*im*b^2*c^5*d^3*Polylogarithms.polylog(2,im*c*x)+-6//5*im*b^2*c^5*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//4*im*b^2*c^3*d^3*x^-2+-1//10*b*c*d^3*x^-4*(a+b*arctan(c*x))+3//2*im*b^2*c^5*d^3*log(1+c^2*x^2)+6//5*im*b^2*c^5*d^3*Polylogarithms.polylog(2,-1*im*c*x)+6//5*b*c^3*d^3*x^-2*(a+b*arctan(c*x))+12//5*a*b*c^5*d^3*log(x)+12//5*b*c^5*d^3*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1//2*im*b*c^2*d^3*x^-3*(a+b*arctan(c*x))+1//20*im*c*d^3*x^-4*(1+im*c*x)^4*(a+b*arctan(c*x))^2+5//2*im*b*c^4*d^3*x^-1*(a+b*arctan(c*x)))
@test integrate(x^-7*(a+b*arctan(c*x))^2*(d+im*c*d*x)^3, x) == :(-1//6*d^3*x^-6*(a+b*arctan(c*x))^2+-113//90*b^2*c^6*d^3*log(1+c^2*x^2)+-14//15*b^2*c^6*d^3*Polylogarithms.polylog(2,-1*im*c*x)+-1//60*b^2*c^2*d^3*x^-4+-1//120*b^2*c^6*d^3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3//4*c^2*d^3*x^-4*(a+b*arctan(c*x))^2+14//15*b^2*c^6*d^3*Polylogarithms.polylog(2,im*c*x)+37//40*b^2*c^6*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+61//180*b^2*c^4*d^3*x^-2+113//45*b^2*c^6*d^3*log(x)+-11//6*b*c^5*d^3*x^-1*(a+b*arctan(c*x))+-3//5*im*c*d^3*x^-5*(a+b*arctan(c*x))^2+-1//10*im*b^2*c^3*d^3*x^-3+-1//15*b*c*d^3*x^-5*(a+b*arctan(c*x))+1//3*im*c^3*d^3*x^-3*(a+b*arctan(c*x))^2+11//18*b*c^3*d^3*x^-3*(a+b*arctan(c*x))+37//30*im*b^2*c^5*d^3*x^-1+37//30*im*b^2*c^6*d^3*arctan(c*x)+-3//10*im*b*c^2*d^3*x^-4*(a+b*arctan(c*x))+1//60*im*b*c^6*d^3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+14//15*im*b*c^4*d^3*x^-2*(a+b*arctan(c*x))+28//15*im*a*b*c^6*d^3*log(x)+37//20*im*b*c^6*d^3*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-1, x) == :(-5//6*c^-4*d^-1*(a+b*arctan(c*x))^2+c^-4*d^-1*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+(1/2)*b^2*c^-4*d^-1*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+(1/2)*b^2*c^-4*d^-1*log(1+c^2*x^2)+(1/2)*c^-2*d^-1*x^2*(a+b*arctan(c*x))^2+-4//3*b^2*c^-4*d^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+im*x*c^-3*d^-1*(a+b*arctan(c*x))^2+-1*a*b*x*c^-3*d^-1+-1*x*b^2*c^-3*d^-1*arctan(c*x)+-1//3*im*x*b^2*c^-3*d^-1+-1//3*im*c^-1*d^-1*x^3*(a+b*arctan(c*x))^2+1//3*im*b^2*c^-4*d^-1*arctan(c*x)+im*b*c^-4*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+1//3*im*b*c^-2*d^-1*x^2*(a+b*arctan(c*x))+8//3*im*b*c^-4*d^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-1, x) == :(x*c^-2*d^-1*(a+b*arctan(c*x))^2+(1/2)*im*c^-3*d^-1*(a+b*arctan(c*x))^2+im*b^2*c^-3*d^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+b*c^-3*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*c^-3*d^-1*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+2*b*c^-3*d^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//2*im*b^2*c^-3*d^-1*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//2*im*b^2*c^-3*d^-1*log(1+c^2*x^2)+-1//2*im*c^-1*d^-1*x^2*(a+b*arctan(c*x))^2+im*a*b*x*c^-2*d^-1+im*x*b^2*c^-2*d^-1*arctan(c*x))
@test integrate(x*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-1, x) == :(c^-2*d^-1*(a+b*arctan(c*x))^2+b^2*c^-2*d^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*c^-2*d^-1*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+-1//2*b^2*c^-2*d^-1*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1*im*x*c^-1*d^-1*(a+b*arctan(c*x))^2+-1*im*b*c^-2*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-2*im*b*c^-2*d^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate((a+b*arctan(c*x))^2*(d+im*c*d*x)^-1, x) == :(im*c^-1*d^-1*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+(1/2)*im*b^2*c^-1*d^-1*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1*b*c^-1*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-1, x) == :(d^-1*(a+b*arctan(c*x))^2*log(2+-2*(1+im*c*x)^-1)+(1/2)*b^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-1, x) == :(-1*d^-1*x^-1*(a+b*arctan(c*x))^2+-1*im*c*d^-1*(a+b*arctan(c*x))^2+b*c*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-1*im*c*b^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-1*im*c*d^-1*(a+b*arctan(c*x))^2*log(2+-2*(1+im*c*x)^-1)+2*b*c*d^-1*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-1//2*im*c*b^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-1, x) == :(-3//2*c^2*d^-1*(a+b*arctan(c*x))^2+-1//2*d^-1*x^-2*(a+b*arctan(c*x))^2+b^2*c^2*d^-1*log(x)+-1*b^2*c^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-1*c^2*d^-1*(a+b*arctan(c*x))^2*log(2+-2*(1+im*c*x)^-1)+-1//2*b^2*c^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1//2*b^2*c^2*d^-1*log(1+c^2*x^2)+im*c*d^-1*x^-1*(a+b*arctan(c*x))^2+-1*b*c*d^-1*x^-1*(a+b*arctan(c*x))+-1*im*b*c^2*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-2*im*b*c^2*d^-1*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1))
@test integrate(x^-4*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-1, x) == :(-1//3*d^-1*x^-3*(a+b*arctan(c*x))^2+c^2*d^-1*x^-1*(a+b*arctan(c*x))^2+-1//3*b^2*c^2*d^-1*x^-1+-1//3*b^2*c^3*d^-1*arctan(c*x)+11//6*im*c^3*d^-1*(a+b*arctan(c*x))^2+im*c^3*d^-1*(a+b*arctan(c*x))^2*log(2+-2*(1+im*c*x)^-1)+(1/2)*im*c*d^-1*x^-2*(a+b*arctan(c*x))^2+(1/2)*im*b^2*c^3*d^-1*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+(1/2)*im*b^2*c^3*d^-1*log(1+c^2*x^2)+-1*im*b^2*c^3*d^-1*log(x)+-1*b*c^3*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-8//3*b*c^3*d^-1*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-1//3*b*c*d^-1*x^-2*(a+b*arctan(c*x))+4//3*im*b^2*c^3*d^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+im*b*c^2*d^-1*x^-1*(a+b*arctan(c*x)))
@test integrate(x^4*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-2, x) == :((1/2)*b^2*c^-5*d^-2*(im+-1*c*x)^-1+-1*c^-5*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+3*x*c^-4*d^-2*(a+b*arctan(c*x))^2+-1//3*x*b^2*c^-4*d^-2+-1//3*c^-2*d^-2*x^3*(a+b*arctan(c*x))^2+-1//6*b^2*c^-5*d^-2*arctan(c*x)+11//6*im*c^-5*d^-2*(a+b*arctan(c*x))^2+-1*im*b^2*c^-5*d^-2*log(1+c^2*x^2)+-1*im*c^-3*d^-2*x^2*(a+b*arctan(c*x))^2+-4*im*c^-5*d^-2*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+-2*im*b^2*c^-5*d^-2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+4*b*c^-5*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+1//3*b*c^-3*d^-2*x^2*(a+b*arctan(c*x))+10//3*im*b^2*c^-5*d^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+20//3*b*c^-5*d^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+im*b*c^-5*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+2*im*a*b*x*c^-4*d^-2+2*im*x*b^2*c^-4*d^-2*arctan(c*x))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-2, x) == :(c^-4*d^-2*(a+b*arctan(c*x))^2+-3*c^-4*d^-2*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+2*b^2*c^-4*d^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-3//2*b^2*c^-4*d^-2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//2*b^2*c^-4*d^-2*log(1+c^2*x^2)+-1//2*c^-2*d^-2*x^2*(a+b*arctan(c*x))^2+im*c^-4*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+a*b*x*c^-3*d^-2+b*c^-4*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+x*b^2*c^-3*d^-2*arctan(c*x)+(1/2)*im*b^2*c^-4*d^-2*arctan(c*x)+-2*im*x*c^-3*d^-2*(a+b*arctan(c*x))^2+-1//2*im*b^2*c^-4*d^-2*(im+-1*c*x)^-1+-4*im*b*c^-4*d^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-3*im*b*c^-4*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-2, x) == :(c^-3*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+(1/2)*b^2*c^-3*d^-2*arctan(c*x)+-1*x*c^-2*d^-2*(a+b*arctan(c*x))^2+-1//2*im*c^-3*d^-2*(a+b*arctan(c*x))^2+-1//2*b^2*c^-3*d^-2*(im+-1*c*x)^-1+im*b^2*c^-3*d^-2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1*im*b^2*c^-3*d^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-2*b*c^-3*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-2*b*c^-3*d^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+2*im*c^-3*d^-2*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+-1*im*b*c^-3*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x)))
@test integrate(x*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-2, x) == :((1/2)*c^-2*d^-2*(a+b*arctan(c*x))^2+c^-2*d^-2*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+(1/2)*b^2*c^-2*d^-2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+(1/2)*im*b^2*c^-2*d^-2*(im+-1*c*x)^-1+-1*im*c^-2*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+-1*b*c^-2*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+-1//2*im*b^2*c^-2*d^-2*arctan(c*x)+im*b*c^-2*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1))
@test integrate((a+b*arctan(c*x))^2*(d+im*c*d*x)^-2, x) == :((1/2)*b^2*c^-1*d^-2*(im+-1*c*x)^-1+-1//2*im*c^-1*d^-2*(a+b*arctan(c*x))^2+-1//2*b^2*c^-1*d^-2*arctan(c*x)+im*c^-1*d^-2*(1+im*c*x)^-1*(a+b*arctan(c*x))^2+im*b*c^-1*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x)))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-2, x) == :(-1//2*d^-2*(a+b*arctan(c*x))^2+d^-2*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+(1/2)*b^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+2*d^-2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+im*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+b*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+(1/2)*im*b^2*d^-2*arctan(c*x)+-1//2*im*b^2*d^-2*(im+-1*c*x)^-1+im*b*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-2, x) == :(-1*d^-2*x^-1*(a+b*arctan(c*x))^2+c*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+(1/2)*c*b^2*d^-2*arctan(c*x)+-1//2*im*c*d^-2*(a+b*arctan(c*x))^2+-1//2*c*b^2*d^-2*(im+-1*c*x)^-1+-1*im*c*b^2*d^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-1*im*c*b^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-4*im*c*d^-2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-2*im*c*d^-2*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+2*b*c*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+2*b*c*d^-2*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-1*im*b*c*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x)))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-2, x) == :(-2*c^2*d^-2*(a+b*arctan(c*x))^2+-1//2*d^-2*x^-2*(a+b*arctan(c*x))^2+b^2*c^2*d^-2*log(x)+-6*c^2*d^-2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-3*c^2*d^-2*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+-2*b^2*c^2*d^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-3//2*b^2*c^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1//2*b^2*c^2*d^-2*log(1+c^2*x^2)+(1/2)*im*b^2*c^2*d^-2*(im+-1*c*x)^-1+-1*im*c^2*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+-1*b*c*d^-2*x^-1*(a+b*arctan(c*x))+-1*b*c^2*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+2*im*c*d^-2*x^-1*(a+b*arctan(c*x))^2+-1//2*im*b^2*c^2*d^-2*arctan(c*x)+-4*im*b*c^2*d^-2*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-3*im*b*c^2*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1))
@test integrate(x^4*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-3, x) == :(-3*x*c^-4*d^-3*(a+b*arctan(c*x))^2+4*c^-5*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+-29//16*b^2*c^-5*d^-3*(im+-1*c*x)^-1+-5//8*im*c^-5*d^-3*(a+b*arctan(c*x))^2+29//16*b^2*c^-5*d^-3*arctan(c*x)+(1/2)*im*b^2*c^-5*d^-3*log(1+c^2*x^2)+(1/2)*im*c^-3*d^-3*x^2*(a+b*arctan(c*x))^2+-6*b*c^-5*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-6*b*c^-5*d^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-3*im*b^2*c^-5*d^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3*im*b^2*c^-5*d^-3*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+6*im*c^-5*d^-3*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+-1//2*im*c^-5*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))^2+-1//4*b*c^-5*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+1//16*im*b^2*c^-5*d^-3*(im+-1*c*x)^-2+-1*im*a*b*x*c^-4*d^-3+-1*im*x*b^2*c^-4*d^-3*arctan(c*x)+-15//4*im*b*c^-5*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x)))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-3, x) == :(3//8*c^-4*d^-3*(a+b*arctan(c*x))^2+-1*b^2*c^-4*d^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3*c^-4*d^-3*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+-1//2*c^-4*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))^2+1//16*b^2*c^-4*d^-3*(im+-1*c*x)^-2+3//2*b^2*c^-4*d^-3*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+im*x*c^-3*d^-3*(a+b*arctan(c*x))^2+-3*im*c^-4*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+-21//16*im*b^2*c^-4*d^-3*arctan(c*x)+-11//4*b*c^-4*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))+21//16*im*b^2*c^-4*d^-3*(im+-1*c*x)^-1+2*im*b*c^-4*d^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+3*im*b*c^-4*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+1//4*im*b*c^-4*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x)))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-3, x) == :(-2*c^-3*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+-13//16*b^2*c^-3*d^-3*arctan(c*x)+-7//8*im*c^-3*d^-3*(a+b*arctan(c*x))^2+13//16*b^2*c^-3*d^-3*(im+-1*c*x)^-1+b*c^-3*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+(1/2)*im*c^-3*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))^2+-1*im*c^-3*d^-3*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+-1//2*im*b^2*c^-3*d^-3*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//16*im*b^2*c^-3*d^-3*(im+-1*c*x)^-2+1//4*b*c^-3*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+7//4*im*b*c^-3*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x)))
@test integrate(x*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-3, x) == :(1//8*c^-2*d^-3*(a+b*arctan(c*x))^2+(1/2)*d^-3*x^2*(1+im*c*x)^-2*(a+b*arctan(c*x))^2+-1//16*b^2*c^-2*d^-3*(im+-1*c*x)^-2+-5//16*im*b^2*c^-2*d^-3*(im+-1*c*x)^-1+3//4*b*c^-2*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))+5//16*im*b^2*c^-2*d^-3*arctan(c*x)+-1//4*im*b*c^-2*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x)))
@test integrate((a+b*arctan(c*x))^2*(d+im*c*d*x)^-3, x) == :(-3//16*b^2*c^-1*d^-3*arctan(c*x)+-1//8*im*c^-1*d^-3*(a+b*arctan(c*x))^2+3//16*b^2*c^-1*d^-3*(im+-1*c*x)^-1+(1/2)*im*c^-1*d^-3*(1+im*c*x)^-2*(a+b*arctan(c*x))^2+-1//4*b*c^-1*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+1//16*im*b^2*c^-1*d^-3*(im+-1*c*x)^-2+1//4*im*b*c^-1*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x)))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-3, x) == :(-5//8*d^-3*(a+b*arctan(c*x))^2+d^-3*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+(1/2)*b^2*d^-3*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+2*d^-3*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))^2+1//16*b^2*d^-3*(im+-1*c*x)^-2+im*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+-11//16*im*b^2*d^-3*(im+-1*c*x)^-1+5//4*b*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))+11//16*im*b^2*d^-3*arctan(c*x)+im*b*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+1//4*im*b*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x)))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+im*c*d*x)^-3, x) == :(-1*d^-3*x^-1*(a+b*arctan(c*x))^2+2*c*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+-19//16*c*b^2*d^-3*(im+-1*c*x)^-1+1//8*im*c*d^-3*(a+b*arctan(c*x))^2+19//16*c*b^2*d^-3*arctan(c*x)+(1/2)*im*c*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))^2+-1*im*c*b^2*d^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-6*im*c*d^-3*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-3*im*c*d^-3*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+2*b*c*d^-3*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+3*b*c*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-3//2*im*c*b^2*d^-3*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1//16*im*c*b^2*d^-3*(im+-1*c*x)^-2+1//4*b*c*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))+-9//4*im*b*c*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x)))
@test integrate((1+im*c*x)^-4*(a+b*arctan(c*x))^2, x) == :(-11//144*b^2*c^-1*arctan(c*x)+-1//24*im*c^-1*(a+b*arctan(c*x))^2+-1//54*b^2*c^-1*(im+-1*c*x)^-3+11//144*b^2*c^-1*(im+-1*c*x)^-1+-1//12*b*c^-1*(im+-1*c*x)^-2*(a+b*arctan(c*x))+1//3*im*c^-1*(1+im*c*x)^-3*(a+b*arctan(c*x))^2+5//144*im*b^2*c^-1*(im+-1*c*x)^-2+-1//9*im*b*c^-1*(im+-1*c*x)^-3*(a+b*arctan(c*x))+1//12*im*b*c^-1*(im+-1*c*x)^-1*(a+b*arctan(c*x)))
@test integrate((c*x+-1*im*a*c*x^2)^-1*arctan(a*x)^2, x) == :((1/2)*c^-1*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+c^-1*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-1*im*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x))
@test integrate((a+b*arctan(c*x))^3*(d+im*c*d*x)^3, x) == :(-3*a*x*b^2*d^3+-3*x*b^3*d^3*arctan(c*x)+3*b^3*c^-1*d^3*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+7*b*c^-1*d^3*(a+b*arctan(c*x))^2+1//4*im*x*b^3*d^3+3//2*b^3*c^-1*d^3*log(1+c^2*x^2)+11//2*b^3*c^-1*d^3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+6*b*c^-1*d^3*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-21//4*im*b*x*d^3*(a+b*arctan(c*x))^2+-1//4*im*b^3*c^-1*d^3*arctan(c*x)+-1//4*im*c^-1*d^3*(1+im*c*x)^4*(a+b*arctan(c*x))^3+3//2*b*c*d^3*x^2*(a+b*arctan(c*x))^2+-11*im*b^2*c^-1*d^3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-6*im*b^2*c^-1*d^3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//4*im*c*b^2*d^3*x^2*(a+b*arctan(c*x))+1//4*im*b*c^2*d^3*x^3*(a+b*arctan(c*x))^2)
@test integrate((a+b*arctan(c*x))^3*(d+im*c*d*x)^2, x) == :((1/2)*b^3*c^-1*d^2*log(1+c^2*x^2)+-1*a*x*b^2*d^2+-1*x*b^3*d^2*arctan(c*x)+2*b^3*c^-1*d^2*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+3*b^3*c^-1*d^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+7//2*b*c^-1*d^2*(a+b*arctan(c*x))^2+(1/2)*b*c*d^2*x^2*(a+b*arctan(c*x))^2+-3*im*b*x*d^2*(a+b*arctan(c*x))^2+4*b*c^-1*d^2*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-1//3*im*c^-1*d^2*(1+im*c*x)^3*(a+b*arctan(c*x))^3+-6*im*b^2*c^-1*d^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-4*im*b^2*c^-1*d^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1))
@test integrate((a+b*arctan(c*x))^3*(d+im*c*d*x), x) == :(3//2*b*d*c^-1*(a+b*arctan(c*x))^2+3//2*d*b^3*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3//2*d*b^3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+3*b*d*c^-1*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-3//2*im*b*d*x*(a+b*arctan(c*x))^2+-1//2*im*d*c^-1*(1+im*c*x)^2*(a+b*arctan(c*x))^3+-3*im*d*b^2*c^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-3*im*d*b^2*c^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate((a+b*arctan(c*x))^3*(d+im*c*d*x)^-1, x) == :(3//4*b^3*c^-1*d^-1*Polylogarithms.polylog(4,1+-2*(1+im*c*x)^-1)+im*c^-1*d^-1*(a+b*arctan(c*x))^3*log(2*(1+im*c*x)^-1)+-3//2*b*c^-1*d^-1*(a+b*arctan(c*x))^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3//2*im*b^2*c^-1*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1))
@test integrate((a+b*arctan(c*x))^3*(d+im*c*d*x)^-2, x) == :(-3//4*b*c^-1*d^-2*(a+b*arctan(c*x))^2+-1//2*im*c^-1*d^-2*(a+b*arctan(c*x))^3+im*c^-1*d^-2*(1+im*c*x)^-1*(a+b*arctan(c*x))^3+-3//4*im*b^3*c^-1*d^-2*(im+-1*c*x)^-1+3//2*b^2*c^-1*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))+3//4*im*b^3*c^-1*d^-2*arctan(c*x)+3//2*im*b*c^-1*d^-2*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2)
@test integrate((a+b*arctan(c*x))^3*(d+im*c*d*x)^-3, x) == :(-9//32*b*c^-1*d^-3*(a+b*arctan(c*x))^2+-1//8*im*c^-1*d^-3*(a+b*arctan(c*x))^3+3//64*b^3*c^-1*d^-3*(im+-1*c*x)^-2+(1/2)*im*c^-1*d^-3*(1+im*c*x)^-2*(a+b*arctan(c*x))^3+-21//64*im*b^3*c^-1*d^-3*(im+-1*c*x)^-1+-3//8*b*c^-1*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x))^2+9//16*b^2*c^-1*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))+21//64*im*b^3*c^-1*d^-3*arctan(c*x)+3//8*im*b*c^-1*d^-3*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+3//16*im*b^2*c^-1*d^-3*(im+-1*c*x)^-2*(a+b*arctan(c*x)))
@test integrate((a+b*arctan(c*x))^3*(d+im*c*d*x)^-4, x) == :(-11//96*b*c^-1*d^-4*(a+b*arctan(c*x))^2+-1//24*im*c^-1*d^-4*(a+b*arctan(c*x))^3+19//576*b^3*c^-1*d^-4*(im+-1*c*x)^-2+-85//576*im*b^3*c^-1*d^-4*(im+-1*c*x)^-1+-1//8*b*c^-1*d^-4*(im+-1*c*x)^-2*(a+b*arctan(c*x))^2+-1//18*b^2*c^-1*d^-4*(im+-1*c*x)^-3*(a+b*arctan(c*x))+1//3*im*c^-1*d^-4*(1+im*c*x)^-3*(a+b*arctan(c*x))^3+1//108*im*b^3*c^-1*d^-4*(im+-1*c*x)^-3+11//48*b^2*c^-1*d^-4*(im+-1*c*x)^-1*(a+b*arctan(c*x))+85//576*im*b^3*c^-1*d^-4*arctan(c*x)+-1//6*im*b*c^-1*d^-4*(im+-1*c*x)^-3*(a+b*arctan(c*x))^2+1//8*im*b*c^-1*d^-4*(im+-1*c*x)^-1*(a+b*arctan(c*x))^2+5//48*im*b^2*c^-1*d^-4*(im+-1*c*x)^-2*(a+b*arctan(c*x)))
@test integrate(x^2*(a+b*arctan(c*x))^3*(d+im*c*d*x)^-1, x) == :(x*c^-2*d^-1*(a+b*arctan(c*x))^3+(1/2)*im*c^-3*d^-1*(a+b*arctan(c*x))^3+-3//2*b*c^-3*d^-1*(a+b*arctan(c*x))^2+-3//2*b^3*c^-3*d^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-3//4*b^3*c^-3*d^-1*Polylogarithms.polylog(4,1+-2*(1+im*c*x)^-1)+3//2*b^3*c^-3*d^-1*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1*im*c^-3*d^-1*(a+b*arctan(c*x))^3*log(2*(1+im*c*x)^-1)+3*b*c^-3*d^-1*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+-1//2*im*c^-1*d^-1*x^2*(a+b*arctan(c*x))^3+3//2*b*c^-3*d^-1*(a+b*arctan(c*x))^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3*im*b^2*c^-3*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3*im*b^2*c^-3*d^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-3//2*im*b^2*c^-3*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+3//2*im*b*x*c^-2*d^-1*(a+b*arctan(c*x))^2)
@test integrate(x*(a+b*arctan(c*x))^3*(d+im*c*d*x)^-1, x) == :(c^-2*d^-1*(a+b*arctan(c*x))^3+-1*c^-2*d^-1*(a+b*arctan(c*x))^3*log(2*(1+im*c*x)^-1)+-1*im*x*c^-1*d^-1*(a+b*arctan(c*x))^3+3*b^2*c^-2*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-3//2*im*b^3*c^-2*d^-1*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-3//2*b^2*c^-2*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+3//4*im*b^3*c^-2*d^-1*Polylogarithms.polylog(4,1+-2*(1+im*c*x)^-1)+-3*im*b*c^-2*d^-1*(a+b*arctan(c*x))^2*log(2*(1+im*c*x)^-1)+-3//2*im*b*c^-2*d^-1*(a+b*arctan(c*x))^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1))
@test integrate((a+b*arctan(c*x))^3*(d+im*c*d*x)^-1, x) == :(3//4*b^3*c^-1*d^-1*Polylogarithms.polylog(4,1+-2*(1+im*c*x)^-1)+im*c^-1*d^-1*(a+b*arctan(c*x))^3*log(2*(1+im*c*x)^-1)+-3//2*b*c^-1*d^-1*(a+b*arctan(c*x))^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+3//2*im*b^2*c^-1*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1))
@test integrate(x^-1*(a+b*arctan(c*x))^3*(d+im*c*d*x)^-1, x) == :(d^-1*(a+b*arctan(c*x))^3*log(2+-2*(1+im*c*x)^-1)+-3//4*im*b^3*d^-1*Polylogarithms.polylog(4,-1+2*(1+im*c*x)^-1)+3//2*b^2*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+3//2*im*b*d^-1*(a+b*arctan(c*x))^2*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1))
@test integrate(x^-2*(a+b*arctan(c*x))^3*(d+im*c*d*x)^-1, x) == :(-1*d^-1*x^-1*(a+b*arctan(c*x))^3+-1*im*c*d^-1*(a+b*arctan(c*x))^3+-3//4*c*b^3*d^-1*Polylogarithms.polylog(4,-1+2*(1+im*c*x)^-1)+3//2*c*b^3*d^-1*Polylogarithms.polylog(3,-1+2*(1+-1*im*c*x)^-1)+-1*im*c*d^-1*(a+b*arctan(c*x))^3*log(2+-2*(1+im*c*x)^-1)+3*b*c*d^-1*(a+b*arctan(c*x))^2*log(2+-2*(1+-1*im*c*x)^-1)+3//2*b*c*d^-1*(a+b*arctan(c*x))^2*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-3*im*c*b^2*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-3//2*im*c*b^2*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1))
@test integrate(x^-3*(a+b*arctan(c*x))^3*(d+im*c*d*x)^-1, x) == :(-3//2*c^2*d^-1*(a+b*arctan(c*x))^3+-1//2*d^-1*x^-2*(a+b*arctan(c*x))^3+-1*c^2*d^-1*(a+b*arctan(c*x))^3*log(2+-2*(1+im*c*x)^-1)+im*c*d^-1*x^-1*(a+b*arctan(c*x))^3+-3*b^2*c^2*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+3*b^2*c^2*d^-1*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-3//2*im*b*c^2*d^-1*(a+b*arctan(c*x))^2+-3//2*im*b^3*c^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-3//2*im*b^3*c^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+-1*im*c*x)^-1)+-3//2*b*c*d^-1*x^-1*(a+b*arctan(c*x))^2+-3//2*b^2*c^2*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+3//4*im*b^3*c^2*d^-1*Polylogarithms.polylog(4,-1+2*(1+im*c*x)^-1)+-3*im*b*c^2*d^-1*(a+b*arctan(c*x))^2*log(2+-2*(1+-1*im*c*x)^-1)+-3//2*im*b*c^2*d^-1*(a+b*arctan(c*x))^2*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1))
@test integrate(x^3*(d+e*x)^-1*(a+b*arctan(c*x)), x) == :(1//3*e^-1*x^3*(a+b*arctan(c*x))+a*x*d^2*e^-3+d^3*e^-4*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1*d^3*e^-4*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1//2*d*e^-2*x^2*(a+b*arctan(c*x))+-1//6*b*c^-1*e^-1*x^2+1//6*b*c^-3*e^-1*log(1+c^2*x^2)+b*x*d^2*e^-3*arctan(c*x)+(1/2)*im*b*d^3*e^-4*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+(1/2)*b*d*x*c^-1*e^-2+-1//2*im*b*d^3*e^-4*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//2*b*d*c^-2*e^-2*arctan(c*x)+-1//2*b*c^-1*d^2*e^-3*log(1+c^2*x^2))
@test integrate(x^2*(d+e*x)^-1*(a+b*arctan(c*x)), x) == :((1/2)*e^-1*x^2*(a+b*arctan(c*x))+d^2*e^-3*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+(1/2)*b*c^-2*e^-1*arctan(c*x)+-1*a*d*x*e^-2+-1*d^2*e^-3*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1//2*b*x*c^-1*e^-1+(1/2)*im*b*d^2*e^-3*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b*d*c^-1*e^-2*log(1+c^2*x^2)+-1*b*d*x*e^-2*arctan(c*x)+-1//2*im*b*d^2*e^-3*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x)))
@test integrate(x*(d+e*x)^-1*(a+b*arctan(c*x)), x) == :(a*x*e^-1+b*x*e^-1*arctan(c*x)+d*e^-2*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1*d*e^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1//2*b*c^-1*e^-1*log(1+c^2*x^2)+(1/2)*im*b*d*e^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1//2*im*b*d*e^-2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1))
@test integrate((d+e*x)^-1*(a+b*arctan(c*x)), x) == :(e^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1*e^-1*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+(1/2)*im*b*e^-1*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//2*im*b*e^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x)))
@test integrate(x^-1*(d+e*x)^-1*(a+b*arctan(c*x)), x) == :(a*d^-1*log(x)+d^-1*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1*d^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+(1/2)*im*b*d^-1*Polylogarithms.polylog(2,-1*im*c*x)+(1/2)*im*b*d^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1//2*im*b*d^-1*Polylogarithms.polylog(2,im*c*x)+-1//2*im*b*d^-1*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1))
@test integrate(x^-2*(d+e*x)^-1*(a+b*arctan(c*x)), x) == :(-1*d^-1*x^-1*(a+b*arctan(c*x))+b*c*d^-1*log(x)+e*d^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1*a*e*d^-2*log(x)+-1*e*d^-2*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1//2*b*c*d^-1*log(1+c^2*x^2)+(1/2)*im*b*e*d^-2*Polylogarithms.polylog(2,im*c*x)+(1/2)*im*b*e*d^-2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//2*im*b*e*d^-2*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*e*d^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x)))
@test integrate(x^-3*(d+e*x)^-1*(a+b*arctan(c*x)), x) == :(-1//2*d^-1*x^-2*(a+b*arctan(c*x))+a*d^-3*e^2*log(x)+e*d^-2*x^-1*(a+b*arctan(c*x))+d^-3*e^2*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1*d^-3*e^2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1//2*b*c*d^-1*x^-1+-1//2*b*c^2*d^-1*arctan(c*x)+(1/2)*im*b*d^-3*e^2*Polylogarithms.polylog(2,-1*im*c*x)+(1/2)*im*b*d^-3*e^2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+(1/2)*b*c*e*d^-2*log(1+c^2*x^2)+-1*b*c*e*d^-2*log(x)+-1//2*im*b*d^-3*e^2*Polylogarithms.polylog(2,im*c*x)+-1//2*im*b*d^-3*e^2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+e*x)^-1, x) == :(1//3*e^-1*x^3*(a+b*arctan(c*x))^2+x*d^2*e^-3*(a+b*arctan(c*x))^2+d^3*e^-4*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+(1/2)*b^2*d^3*e^-4*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+-1*d^3*e^-4*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1//2*d*c^-2*e^-2*(a+b*arctan(c*x))^2+-1//2*d*e^-2*x^2*(a+b*arctan(c*x))^2+-1//2*b^2*d^3*e^-4*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1//3*im*c^-3*e^-1*(a+b*arctan(c*x))^2+-1//3*b^2*c^-3*e^-1*arctan(c*x)+1//3*x*b^2*c^-2*e^-1+im*c^-1*d^2*e^-3*(a+b*arctan(c*x))^2+-2//3*b*c^-3*e^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//2*d*b^2*c^-2*e^-2*log(1+c^2*x^2)+-1//3*im*b^2*c^-3*e^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//3*b*c^-1*e^-1*x^2*(a+b*arctan(c*x))+im*b*d^3*e^-4*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+im*b^2*c^-1*d^2*e^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+a*b*d*x*c^-1*e^-2+d*x*b^2*c^-1*e^-2*arctan(c*x)+-1*im*b*d^3*e^-4*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+2*b*c^-1*d^2*e^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+e*x)^-1, x) == :((1/2)*c^-2*e^-1*(a+b*arctan(c*x))^2+(1/2)*e^-1*x^2*(a+b*arctan(c*x))^2+d^2*e^-3*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+(1/2)*b^2*c^-2*e^-1*log(1+c^2*x^2)+(1/2)*b^2*d^2*e^-3*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1*d*x*e^-2*(a+b*arctan(c*x))^2+-1*d^2*e^-3*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-1//2*b^2*d^2*e^-3*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+-1*im*d*c^-1*e^-2*(a+b*arctan(c*x))^2+-1*a*b*x*c^-1*e^-1+-1*x*b^2*c^-1*e^-1*arctan(c*x)+im*b*d^2*e^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1*im*b*d^2*e^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1*im*d*b^2*c^-1*e^-2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-2*b*d*c^-1*e^-2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x*(a+b*arctan(c*x))^2*(d+e*x)^-1, x) == :(x*e^-1*(a+b*arctan(c*x))^2+im*c^-1*e^-1*(a+b*arctan(c*x))^2+d*e^-2*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+(1/2)*d*b^2*e^-2*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+-1*d*e^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1//2*d*b^2*e^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+im*b^2*c^-1*e^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*b*c^-1*e^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+im*b*d*e^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1*im*b*d*e^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1))
@test integrate((a+b*arctan(c*x))^2*(d+e*x)^-1, x) == :(e^-1*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+(1/2)*b^2*e^-1*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1*e^-1*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-1//2*b^2*e^-1*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+im*b*e^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1*im*b*e^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x)))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+e*x)^-1, x) == :(d^-1*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+(1/2)*b^2*d^-1*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1*d^-1*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+2*d^-1*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*b^2*d^-1*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//2*b^2*d^-1*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-1*im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+e*x)^-1, x) == :(-1*d^-1*x^-1*(a+b*arctan(c*x))^2+e*d^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+(1/2)*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+(1/2)*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1*im*c*d^-1*(a+b*arctan(c*x))^2+-1*e*d^-2*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-2*e*d^-2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+-1//2*e*b^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1*im*c*b^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+2*b*c*d^-1*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+im*b*e*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+im*b*e*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1*im*b*e*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+-1*im*b*e*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+e*x)^-1, x) == :(-1//2*c^2*d^-1*(a+b*arctan(c*x))^2+-1//2*d^-1*x^-2*(a+b*arctan(c*x))^2+e*d^-2*x^-1*(a+b*arctan(c*x))^2+b^2*c^2*d^-1*log(x)+d^-3*e^2*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+(1/2)*b^2*d^-3*e^2*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b^2*d^-3*e^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1*d^-3*e^2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+2*d^-3*e^2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*b^2*c^2*d^-1*log(1+c^2*x^2)+-1//2*b^2*d^-3*e^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//2*b^2*d^-3*e^2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+im*c*e*d^-2*(a+b*arctan(c*x))^2+-1*b*c*d^-1*x^-1*(a+b*arctan(c*x))+im*b*d^-3*e^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e+c*d)^-1*(d+e*x))+im*b*d^-3*e^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+im*c*e*b^2*d^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+-1*im*b*d^-3*e^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*b*d^-3*e^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-2*b*c*e*d^-2*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1))
@test integrate(x^3*(c+c*a^2*x^2)*arctan(a*x), x) == :(-1//12*c*a^-4*arctan(a*x)+-1//30*a*c*x^5+-1//36*c*a^-1*x^3+1//4*c*x^4*arctan(a*x)+1//12*c*x*a^-3+1//6*c*a^2*x^6*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)*arctan(a*x), x) == :(-1//15*c*a^-1*x^2+-1//20*a*c*x^4+1//3*c*x^3*arctan(a*x)+1//15*c*a^-3*log(1+a^2*x^2)+1//5*c*a^2*x^5*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)*arctan(a*x), x) == :(-1//4*c*x*a^-1+-1//12*a*c*x^3+1//4*c*a^-2*(1+a^2*x^2)^2*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)*arctan(a*x), x) == :((1/2)*c*arctan(a*x)+(1/2)*im*c*Polylogarithms.polylog(2,-1*im*a*x)+-1//2*im*c*Polylogarithms.polylog(2,im*a*x)+-1//2*a*c*x+(1/2)*c*a^2*x^2*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)*arctan(a*x), x) == :(a*c*log(x)+-1*a*c*log(1+a^2*x^2)+-1*c*x^-1*arctan(a*x)+c*x*a^2*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)*arctan(a*x), x) == :(-1//2*a*c*x^-1+-1//2*c*a^2*arctan(a*x)+-1//2*c*x^-2*arctan(a*x)+(1/2)*im*c*a^2*Polylogarithms.polylog(2,-1*im*a*x)+-1//2*im*c*a^2*Polylogarithms.polylog(2,im*a*x))
@test integrate(x^-4*(c+c*a^2*x^2)*arctan(a*x), x) == :(-1//3*c*a^3*log(1+a^2*x^2)+-1//3*c*x^-3*arctan(a*x)+-1//6*a*c*x^-2+2//3*c*a^3*log(x)+-1*c*a^2*x^-1*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^2*arctan(a*x), x) == :(-1//24*a*c^2*x^5+-1//24*a^-4*c^2*arctan(a*x)+-1//56*a^3*c^2*x^7+-1//72*a^-1*c^2*x^3+1//4*c^2*x^4*arctan(a*x)+1//24*x*a^-3*c^2+1//3*a^2*c^2*x^6*arctan(a*x)+1//8*a^4*c^2*x^8*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^2*arctan(a*x), x) == :(-9//140*a*c^2*x^4+-4//105*a^-1*c^2*x^2+-1//42*a^3*c^2*x^6+1//3*c^2*x^3*arctan(a*x)+4//105*a^-3*c^2*log(1+a^2*x^2)+1//7*a^4*c^2*x^7*arctan(a*x)+2//5*a^2*c^2*x^5*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^2*arctan(a*x), x) == :(-1//6*x*a^-1*c^2+-1//9*a*c^2*x^3+-1//30*a^3*c^2*x^5+1//6*a^-2*c^2*(1+a^2*x^2)^3*arctan(a*x))
@test integrate((c+c*a^2*x^2)^2*arctan(a*x), x) == :(-4//15*a^-1*c^2*log(1+a^2*x^2)+-2//15*a^-1*c^2*(1+a^2*x^2)+-1//20*a^-1*c^2*(1+a^2*x^2)^2+8//15*x*c^2*arctan(a*x)+1//5*x*c^2*(1+a^2*x^2)^2*arctan(a*x)+4//15*x*c^2*(1+a^2*x^2)*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^2*arctan(a*x), x) == :(3//4*c^2*arctan(a*x)+(1/2)*im*c^2*Polylogarithms.polylog(2,-1*im*a*x)+-3//4*a*x*c^2+-1//2*im*c^2*Polylogarithms.polylog(2,im*a*x)+-1//12*a^3*c^2*x^3+a^2*c^2*x^2*arctan(a*x)+1//4*a^4*c^2*x^4*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^2*arctan(a*x), x) == :(a*c^2*log(x)+-1*c^2*x^-1*arctan(a*x)+-4//3*a*c^2*log(1+a^2*x^2)+-1//6*a^3*c^2*x^2+2*x*a^2*c^2*arctan(a*x)+1//3*a^4*c^2*x^3*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^2*arctan(a*x), x) == :(-1//2*a*c^2*x^-1+-1//2*x*a^3*c^2+-1//2*c^2*x^-2*arctan(a*x)+im*a^2*c^2*Polylogarithms.polylog(2,-1*im*a*x)+(1/2)*a^4*c^2*x^2*arctan(a*x)+-1*im*a^2*c^2*Polylogarithms.polylog(2,im*a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^2*arctan(a*x), x) == :(-4//3*a^3*c^2*log(1+a^2*x^2)+-1//3*c^2*x^-3*arctan(a*x)+-1//6*a*c^2*x^-2+5//3*a^3*c^2*log(x)+x*a^4*c^2*arctan(a*x)+-2*a^2*c^2*x^-1*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^3*arctan(a*x), x) == :(-11//280*a^3*c^3*x^7+-9//200*a*c^3*x^5+-1//40*a^-4*c^3*arctan(a*x)+-1//90*a^5*c^3*x^9+-1//120*a^-1*c^3*x^3+1//4*c^3*x^4*arctan(a*x)+1//40*x*a^-3*c^3+(1/2)*a^2*c^3*x^6*arctan(a*x)+1//10*a^6*c^3*x^10*arctan(a*x)+3//8*a^4*c^3*x^8*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^3*arctan(a*x), x) == :(-89//1260*a*c^3*x^4+-10//189*a^3*c^3*x^6+-8//315*a^-1*c^3*x^2+-1//72*a^5*c^3*x^8+1//3*c^3*x^3*arctan(a*x)+8//315*a^-3*c^3*log(1+a^2*x^2)+1//9*a^6*c^3*x^9*arctan(a*x)+3//5*a^2*c^3*x^5*arctan(a*x)+3//7*a^4*c^3*x^7*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^3*arctan(a*x), x) == :(-3//40*a^3*c^3*x^5+-1//8*a*c^3*x^3+-1//8*x*a^-1*c^3+-1//56*a^5*c^3*x^7+1//8*a^-2*c^3*(1+a^2*x^2)^4*arctan(a*x))
@test integrate((c+c*a^2*x^2)^3*arctan(a*x), x) == :(-8//35*a^-1*c^3*log(1+a^2*x^2)+-4//35*a^-1*c^3*(1+a^2*x^2)+-3//70*a^-1*c^3*(1+a^2*x^2)^2+-1//42*a^-1*c^3*(1+a^2*x^2)^3+16//35*x*c^3*arctan(a*x)+1//7*x*c^3*(1+a^2*x^2)^3*arctan(a*x)+6//35*x*c^3*(1+a^2*x^2)^2*arctan(a*x)+8//35*x*c^3*(1+a^2*x^2)*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^3*arctan(a*x), x) == :(11//12*c^3*arctan(a*x)+(1/2)*im*c^3*Polylogarithms.polylog(2,-1*im*a*x)+-11//12*a*x*c^3+-7//36*a^3*c^3*x^3+-1//2*im*c^3*Polylogarithms.polylog(2,im*a*x)+-1//30*a^5*c^3*x^5+1//6*a^6*c^3*x^6*arctan(a*x)+3//2*a^2*c^3*x^2*arctan(a*x)+3//4*a^4*c^3*x^4*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^3*arctan(a*x), x) == :(a*c^3*log(x)+-1*c^3*x^-1*arctan(a*x)+-8//5*a*c^3*log(1+a^2*x^2)+-2//5*a^3*c^3*x^2+-1//20*a^5*c^3*x^4+a^4*c^3*x^3*arctan(a*x)+3*x*a^2*c^3*arctan(a*x)+1//5*a^6*c^3*x^5*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^3*arctan(a*x), x) == :(-5//4*x*a^3*c^3+-1//2*a*c^3*x^-1+-1//2*c^3*x^-2*arctan(a*x)+-1//12*a^5*c^3*x^3+3//4*a^2*c^3*arctan(a*x)+-3//2*im*a^2*c^3*Polylogarithms.polylog(2,im*a*x)+1//4*a^6*c^3*x^4*arctan(a*x)+3//2*im*a^2*c^3*Polylogarithms.polylog(2,-1*im*a*x)+3//2*a^4*c^3*x^2*arctan(a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^3*arctan(a*x), x) == :(-8//3*a^3*c^3*log(1+a^2*x^2)+-1//3*c^3*x^-3*arctan(a*x)+-1//6*a*c^3*x^-2+-1//6*a^5*c^3*x^2+8//3*a^3*c^3*log(x)+-3*a^2*c^3*x^-1*arctan(a*x)+3*x*a^4*c^3*arctan(a*x)+1//3*a^6*c^3*x^3*arctan(a*x))
@test integrate(x^4*(c+c*a^2*x^2)^-1*arctan(a*x), x) == :((1/2)*a^-5*c^-1*arctan(a*x)^2+-1//6*a^-3*c^-1*x^2+2//3*a^-5*c^-1*log(1+a^2*x^2)+-1*x*a^-4*c^-1*arctan(a*x)+1//3*a^-2*c^-1*x^3*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-1*arctan(a*x), x) == :((1/2)*a^-4*c^-1*arctan(a*x)+-1//2*x*a^-3*c^-1+a^-4*c^-1*arctan(a*x)*log(2*(1+im*a*x)^-1)+(1/2)*im*a^-4*c^-1*arctan(a*x)^2+(1/2)*im*a^-4*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+(1/2)*a^-2*c^-1*x^2*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-1*arctan(a*x), x) == :(-1//2*a^-3*c^-1*arctan(a*x)^2+-1//2*a^-3*c^-1*log(1+a^2*x^2)+x*a^-2*c^-1*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-1*arctan(a*x), x) == :(-1*a^-2*c^-1*arctan(a*x)*log(2*(1+im*a*x)^-1)+-1//2*im*a^-2*c^-1*arctan(a*x)^2+-1//2*im*a^-2*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x), x) == :((1/2)*a^-1*c^-1*arctan(a*x)^2)
@test integrate(x^-1*(c+c*a^2*x^2)^-1*arctan(a*x), x) == :(c^-1*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-1//2*im*c^-1*arctan(a*x)^2+-1//2*im*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1))
@test integrate(x^-2*(c+c*a^2*x^2)^-1*arctan(a*x), x) == :(a*c^-1*log(x)+-1*c^-1*x^-1*arctan(a*x)+-1//2*a*c^-1*arctan(a*x)^2+-1//2*a*c^-1*log(1+a^2*x^2))
@test integrate(x^-3*(c+c*a^2*x^2)^-1*arctan(a*x), x) == :(-1//2*a*c^-1*x^-1+-1//2*a^2*c^-1*arctan(a*x)+-1//2*c^-1*x^-2*arctan(a*x)+(1/2)*im*a^2*c^-1*arctan(a*x)^2+(1/2)*im*a^2*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-1*a^2*c^-1*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1))
@test integrate(x^-4*(c+c*a^2*x^2)^-1*arctan(a*x), x) == :((1/2)*a^3*c^-1*arctan(a*x)^2+-4//3*a^3*c^-1*log(x)+-1//3*c^-1*x^-3*arctan(a*x)+-1//6*a*c^-1*x^-2+2//3*a^3*c^-1*log(1+a^2*x^2)+a^2*c^-1*x^-1*arctan(a*x))
@test integrate(x^5*(c+c*a^2*x^2)^-2*arctan(a*x), x) == :(-1//2*x*a^-5*c^-2+3//4*a^-6*c^-2*arctan(a*x)+im*a^-6*c^-2*arctan(a*x)^2+im*a^-6*c^-2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+(1/2)*a^-4*c^-2*x^2*arctan(a*x)+2*a^-6*c^-2*arctan(a*x)*log(2*(1+im*a*x)^-1)+-1//2*a^-6*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+1//4*x*a^-5*c^-2*(1+a^2*x^2)^-1)
@test integrate(x^4*(c+c*a^2*x^2)^-2*arctan(a*x), x) == :(-3//4*a^-5*c^-2*arctan(a*x)^2+-1//2*a^-5*c^-2*log(1+a^2*x^2)+1//4*a^-5*c^-2*(1+a^2*x^2)^-1+x*a^-4*c^-2*arctan(a*x)+(1/2)*x*a^-4*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-2*arctan(a*x), x) == :(-1//4*a^-4*c^-2*arctan(a*x)+(1/2)*a^-4*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+-1*a^-4*c^-2*arctan(a*x)*log(2*(1+im*a*x)^-1)+-1//2*im*a^-4*c^-2*arctan(a*x)^2+-1//2*im*a^-4*c^-2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-1//4*x*a^-3*c^-2*(1+a^2*x^2)^-1)
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x), x) == :(-1//4*a^-3*c^-2*(1+a^2*x^2)^-1+1//4*a^-3*c^-2*arctan(a*x)^2+-1//2*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x), x) == :(1//4*a^-2*c^-2*arctan(a*x)+-1//2*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+1//4*x*a^-1*c^-2*(1+a^2*x^2)^-1)
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x), x) == :(1//4*a^-1*c^-2*(1+a^2*x^2)^-1+1//4*a^-1*c^-2*arctan(a*x)^2+(1/2)*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^-2*arctan(a*x), x) == :(-1//4*c^-2*arctan(a*x)+c^-2*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+(1/2)*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+-1//2*im*c^-2*arctan(a*x)^2+-1//2*im*c^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-1//4*a*x*c^-2*(1+a^2*x^2)^-1)
@test integrate(x^-2*(c+c*a^2*x^2)^-2*arctan(a*x), x) == :(a*c^-2*log(x)+-1*c^-2*x^-1*arctan(a*x)+-3//4*a*c^-2*arctan(a*x)^2+-1//2*a*c^-2*log(1+a^2*x^2)+-1//4*a*c^-2*(1+a^2*x^2)^-1+-1//2*x*a^2*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^-2*arctan(a*x), x) == :(-1//2*a*c^-2*x^-1+-1//2*c^-2*x^-2*arctan(a*x)+-1//4*a^2*c^-2*arctan(a*x)+im*a^2*c^-2*arctan(a*x)^2+im*a^2*c^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-2*a^2*c^-2*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-1//2*a^2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+1//4*x*a^3*c^-2*(1+a^2*x^2)^-1)
@test integrate(x^-4*(c+c*a^2*x^2)^-2*arctan(a*x), x) == :(-7//3*a^3*c^-2*log(x)+-1//3*c^-2*x^-3*arctan(a*x)+-1//6*a*c^-2*x^-2+1//4*a^3*c^-2*(1+a^2*x^2)^-1+5//4*a^3*c^-2*arctan(a*x)^2+7//6*a^3*c^-2*log(1+a^2*x^2)+2*a^2*c^-2*x^-1*arctan(a*x)+(1/2)*x*a^4*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x), x) == :(-3//32*a^-4*c^-3*arctan(a*x)+1//4*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)+1//16*a^-1*c^-3*x^3*(1+a^2*x^2)^-2+3//32*x*a^-3*c^-3*(1+a^2*x^2)^-1)
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x), x) == :(-1//16*a^-3*c^-3*(1+a^2*x^2)^-2+1//16*a^-3*c^-3*(1+a^2*x^2)^-1+1//16*a^-3*c^-3*arctan(a*x)^2+-1//4*x*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+1//8*x*a^-2*c^-3*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x), x) == :(3//32*a^-2*c^-3*arctan(a*x)+-1//4*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+1//16*x*a^-1*c^-3*(1+a^2*x^2)^-2+3//32*x*a^-1*c^-3*(1+a^2*x^2)^-1)
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x), x) == :(1//16*a^-1*c^-3*(1+a^2*x^2)^-2+3//16*a^-1*c^-3*(1+a^2*x^2)^-1+3//16*a^-1*c^-3*arctan(a*x)^2+1//4*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+3//8*x*c^-3*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^-3*arctan(a*x), x) == :(-11//32*c^-3*arctan(a*x)+c^-3*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+(1/2)*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+-1//2*im*c^-3*arctan(a*x)^2+-1//2*im*c^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+1//4*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+-11//32*a*x*c^-3*(1+a^2*x^2)^-1+-1//16*a*x*c^-3*(1+a^2*x^2)^-2)
@test integrate(x^-2*(c+c*a^2*x^2)^-3*arctan(a*x), x) == :(a*c^-3*log(x)+-1*c^-3*x^-1*arctan(a*x)+-15//16*a*c^-3*arctan(a*x)^2+-7//16*a*c^-3*(1+a^2*x^2)^-1+-1//2*a*c^-3*log(1+a^2*x^2)+-1//16*a*c^-3*(1+a^2*x^2)^-2+-7//8*x*a^2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+-1//4*x*a^2*c^-3*(1+a^2*x^2)^-2*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^-3*arctan(a*x), x) == :(-1//2*a*c^-3*x^-1+-1//2*c^-3*x^-2*arctan(a*x)+3//32*a^2*c^-3*arctan(a*x)+-1*a^2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+-3*a^2*c^-3*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-1//4*a^2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+1//16*x*a^3*c^-3*(1+a^2*x^2)^-2+3//2*im*a^2*c^-3*arctan(a*x)^2+3//2*im*a^2*c^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+19//32*x*a^3*c^-3*(1+a^2*x^2)^-1)
@test integrate(x^-4*(c+c*a^2*x^2)^-3*arctan(a*x), x) == :(-10//3*a^3*c^-3*log(x)+-1//3*c^-3*x^-3*arctan(a*x)+-1//6*a*c^-3*x^-2+1//16*a^3*c^-3*(1+a^2*x^2)^-2+5//3*a^3*c^-3*log(1+a^2*x^2)+11//16*a^3*c^-3*(1+a^2*x^2)^-1+35//16*a^3*c^-3*arctan(a*x)^2+3*a^2*c^-3*x^-1*arctan(a*x)+1//4*x*a^4*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+11//8*x*a^4*c^-3*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x), x) == :(-2//15*a^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//20*a^-1*x^3*(c+c*a^2*x^2)^(1/2)+1//5*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//24*x*a^-3*(c+c*a^2*x^2)^(1/2)+11//120*a^-4*c^(1/2)*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//15*a^-2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x), x) == :(1//8*a^-3*(c+c*a^2*x^2)^(1/2)+-1//12*a^-3*c^-1*(c+c*a^2*x^2)^3//2+1//4*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//8*x*a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//8*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+1//8*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+1//4*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x*(c+c*a^2*x^2)^(1/2)*arctan(a*x), x) == :(-1//6*x*a^-1*(c+c*a^2*x^2)^(1/2)+-1//6*a^-2*c^(1/2)*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//3*a^-2*c^-1*(c+c*a^2*x^2)^3//2*arctan(a*x))
@test integrate((c+c*a^2*x^2)^(1/2)*arctan(a*x), x) == :(-1//2*a^-1*(c+c*a^2*x^2)^(1/2)+(1/2)*x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+(1/2)*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1//2*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x), x) == :((c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1*c^(1/2)*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x), x) == :(-1*a*c^(1/2)*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x), x) == :(-1//2*a*x^-1*(c+c*a^2*x^2)^(1/2)+-1//2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+(1/2)*im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1//2*im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x), x) == :(-1//6*a*x^-2*(c+c*a^2*x^2)^(1/2)+-1//6*a^3*c^(1/2)*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1//3*c^-1*x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^3//2*arctan(a*x), x) == :(17//560*a^-4*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-23//840*c*a^-1*x^3*(c+c*a^2*x^2)^(1/2)+-2//35*c*a^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//42*a*c*x^5*(c+c*a^2*x^2)^(1/2)+3//112*c*x*a^-3*(c+c*a^2*x^2)^(1/2)+8//35*c*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//7*c*a^2*x^6*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//35*c*a^-2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^3//2*arctan(a*x), x) == :(1//72*a^-3*(c+c*a^2*x^2)^3//2+-1//30*a^-3*c^-1*(c+c*a^2*x^2)^5//2+1//16*c*a^-3*(c+c*a^2*x^2)^(1/2)+7//24*c*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//6*c*a^2*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//16*c*x*a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//16*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+1//16*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+1//8*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x*(c+c*a^2*x^2)^3//2*arctan(a*x), x) == :(-3//40*a^-2*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-1//20*x*a^-1*(c+c*a^2*x^2)^3//2+-3//40*c*x*a^-1*(c+c*a^2*x^2)^(1/2)+1//5*a^-2*c^-1*(c+c*a^2*x^2)^5//2*arctan(a*x))
@test integrate((c+c*a^2*x^2)^3//2*arctan(a*x), x) == :(-1//12*a^-1*(c+c*a^2*x^2)^3//2+-3//8*c*a^-1*(c+c*a^2*x^2)^(1/2)+1//4*x*(c+c*a^2*x^2)^3//2*arctan(a*x)+3//8*c*x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-3//8*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3//8*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3//4*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-1*(c+c*a^2*x^2)^3//2*arctan(a*x), x) == :(-7//6*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//3*(c+c*a^2*x^2)^3//2*arctan(a*x)+c*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//6*a*c*x*(c+c*a^2*x^2)^(1/2)+im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-2*(c+c*a^2*x^2)^3//2*arctan(a*x), x) == :(-1*a*c^3//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1//2*a*c*(c+c*a^2*x^2)^(1/2)+-1*c*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+(1/2)*c*x*a^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-3//2*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3//2*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x), x) == :(-1*a^2*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+c*a^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//2*a*c*x^-1*(c+c*a^2*x^2)^(1/2)+-1//2*c*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-3*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3//2*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3//2*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-4*(c+c*a^2*x^2)^3//2*arctan(a*x), x) == :(-7//6*a^3*c^3//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1//3*x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)+-1//6*a*c*x^-2*(c+c*a^2*x^2)^(1/2)+-1*c*a^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^3*(c+c*a^2*x^2)^5//2*arctan(a*x), x) == :(115//8064*a^-4*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-205//12096*a^-1*c^2*x^3*(c+c*a^2*x^2)^(1/2)+-103//3024*a*c^2*x^5*(c+c*a^2*x^2)^(1/2)+-2//63*a^-4*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//72*a^3*c^2*x^7*(c+c*a^2*x^2)^(1/2)+5//21*c^2*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+47//2688*x*a^-3*c^2*(c+c*a^2*x^2)^(1/2)+1//9*a^4*c^2*x^8*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//63*a^-2*c^2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+19//63*a^2*c^2*x^6*(c+c*a^2*x^2)^(1/2)*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^5//2*arctan(a*x), x) == :(1//240*a^-3*(c+c*a^2*x^2)^5//2+-1//56*a^-3*c^-1*(c+c*a^2*x^2)^7//2+5//128*a^-3*c^2*(c+c*a^2*x^2)^(1/2)+5//576*c*a^-3*(c+c*a^2*x^2)^3//2+59//192*c^2*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//8*a^4*c^2*x^7*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+5//128*x*a^-2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+17//48*a^2*c^2*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5//128*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+5//128*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+5//64*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x*(c+c*a^2*x^2)^5//2*arctan(a*x), x) == :(-5//112*a^-2*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-1//42*x*a^-1*(c+c*a^2*x^2)^5//2+-5//112*x*a^-1*c^2*(c+c*a^2*x^2)^(1/2)+-5//168*c*x*a^-1*(c+c*a^2*x^2)^3//2+1//7*a^-2*c^-1*(c+c*a^2*x^2)^7//2*arctan(a*x))
@test integrate((c+c*a^2*x^2)^5//2*arctan(a*x), x) == :(-1//30*a^-1*(c+c*a^2*x^2)^5//2+-5//16*a^-1*c^2*(c+c*a^2*x^2)^(1/2)+-5//72*c*a^-1*(c+c*a^2*x^2)^3//2+1//6*x*(c+c*a^2*x^2)^5//2*arctan(a*x)+5//16*x*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+5//24*c*x*(c+c*a^2*x^2)^3//2*arctan(a*x)+-5//16*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+5//16*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-5//8*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-1*(c+c*a^2*x^2)^5//2*arctan(a*x), x) == :(-149//120*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//5*(c+c*a^2*x^2)^5//2*arctan(a*x)+c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//3*c*(c+c*a^2*x^2)^3//2*arctan(a*x)+-29//120*a*x*c^2*(c+c*a^2*x^2)^(1/2)+-1//20*a*c*x*(c+c*a^2*x^2)^3//2+im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-2*(c+c*a^2*x^2)^5//2*arctan(a*x), x) == :(-1*a*c^5//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-7//8*a*c^2*(c+c*a^2*x^2)^(1/2)+-1//12*a*c*(c+c*a^2*x^2)^3//2+-1*c^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//4*c*x*a^2*(c+c*a^2*x^2)^3//2*arctan(a*x)+7//8*x*a^2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-15//8*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+15//8*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-15//4*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-3*(c+c*a^2*x^2)^5//2*arctan(a*x), x) == :(-13//6*a^2*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+2*a^2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//2*a*c^2*x^-1*(c+c*a^2*x^2)^(1/2)+-1//2*c^2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//6*x*a^3*c^2*(c+c*a^2*x^2)^(1/2)+1//3*c*a^2*(c+c*a^2*x^2)^3//2*arctan(a*x)+-5*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-5//2*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+5//2*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-4*(c+c*a^2*x^2)^5//2*arctan(a*x), x) == :(-13//6*a^3*c^5//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1//2*a^3*c^2*(c+c*a^2*x^2)^(1/2)+-1//3*c*x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)+-1//6*a*c^2*x^-2*(c+c*a^2*x^2)^(1/2)+(1/2)*x*a^4*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-2*a^2*c^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5//2*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+5//2*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-5*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^3*(c+c*a^2*x^2)^-1//2*arctan(a*x), x) == :(5//6*a^-4*c^-1//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-2//3*a^-4*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//6*x*a^-3*c^-1*(c+c*a^2*x^2)^(1/2)+1//3*a^-2*c^-1*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-1//2*arctan(a*x), x) == :(-1//2*a^-3*c^-1*(c+c*a^2*x^2)^(1/2)+(1/2)*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+(1/2)*x*a^-2*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//2*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x*(c+c*a^2*x^2)^-1//2*arctan(a*x), x) == :(-1*a^-2*c^-1//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+a^-2*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x))
@test integrate((c+c*a^2*x^2)^-1//2*arctan(a*x), x) == :(im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x), x) == :(im*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x), x) == :(-1*a*c^-1//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^-1//2*arctan(a*x), x) == :(-1//2*a*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)+-1//2*c^-1*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+(1/2)*im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1//2*im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-4*(c+c*a^2*x^2)^-1//2*arctan(a*x), x) == :(5//6*a^3*c^-1//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1//3*c^-1*x^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//6*a*c^-1*x^-2*(c+c*a^2*x^2)^(1/2)+2//3*a^2*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x), x) == :(-1*a^-4*c^-3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+a^-4*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+a^-4*c^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1*x*a^-3*c^-1*(c+c*a^2*x^2)^-1//2)
@test integrate(x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x), x) == :(-1*a^-3*c^-1*(c+c*a^2*x^2)^-1//2+-1*x*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x), x) == :(x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2+-1*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x), x) == :(a^-1*c^-1*(c+c*a^2*x^2)^-1//2+x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x), x) == :(c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-1*a*x*c^-1*(c+c*a^2*x^2)^-1//2+im*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-2*(c+c*a^2*x^2)^-3//2*arctan(a*x), x) == :(-1*a*c^-1*(c+c*a^2*x^2)^-1//2+-1*a*c^-3//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1*c^-2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1*x*a^2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^-3//2*arctan(a*x), x) == :(x*a^3*c^-1*(c+c*a^2*x^2)^-1//2+-1*a^2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-1//2*a*c^-2*x^-1*(c+c*a^2*x^2)^(1/2)+-1//2*c^-2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+3*a^2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3//2*im*a^2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3//2*im*a^2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-4*(c+c*a^2*x^2)^-3//2*arctan(a*x), x) == :(a^3*c^-1*(c+c*a^2*x^2)^-1//2+11//6*a^3*c^-3//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1//3*c^-2*x^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//6*a*c^-2*x^-2*(c+c*a^2*x^2)^(1/2)+x*a^4*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+5//3*a^2*c^-2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x))
@test integrate(x^5*(c+c*a^2*x^2)^-5//2*arctan(a*x), x) == :(-1*a^-6*c^-5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+a^-6*c^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5//3*x*a^-5*c^-2*(c+c*a^2*x^2)^-1//2+-1//9*a^-3*c^-1*x^3*(c+c*a^2*x^2)^-3//2+5//3*a^-6*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+1//3*a^-4*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x))
@test integrate(x^4*(c+c*a^2*x^2)^-5//2*arctan(a*x), x) == :(-4//3*a^-5*c^-2*(c+c*a^2*x^2)^-1//2+1//9*a^-5*c^-1*(c+c*a^2*x^2)^-3//2+-1*x*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-1//3*a^-2*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)+im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x), x) == :(-2//3*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+1//9*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2+2//3*x*a^-3*c^-2*(c+c*a^2*x^2)^-1//2+-1//3*a^-2*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x), x) == :(-1//9*a^-3*c^-1*(c+c*a^2*x^2)^-3//2+1//3*a^-3*c^-2*(c+c*a^2*x^2)^-1//2+1//3*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x), x) == :(-1//3*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+1//9*x*a^-1*c^-1*(c+c*a^2*x^2)^-3//2+2//9*x*a^-1*c^-2*(c+c*a^2*x^2)^-1//2)
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x), x) == :(1//9*a^-1*c^-1*(c+c*a^2*x^2)^-3//2+2//3*a^-1*c^-2*(c+c*a^2*x^2)^-1//2+1//3*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+2//3*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^-5//2*arctan(a*x), x) == :(c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+1//3*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+-11//9*a*x*c^-2*(c+c*a^2*x^2)^-1//2+-1//9*a*x*c^-1*(c+c*a^2*x^2)^-3//2+im*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1*im*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-2*(c+c*a^2*x^2)^-5//2*arctan(a*x), x) == :(-1*a*c^-5//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-5//3*a*c^-2*(c+c*a^2*x^2)^-1//2+-1//9*a*c^-1*(c+c*a^2*x^2)^-3//2+-1*c^-3*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5//3*x*a^2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-1//3*x*a^2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x))
@test integrate(x^3*arctan(a*x)^2*(c+c*a^2*x^2), x) == :(1//60*c*x^4+-7//90*c*a^-4*log(1+a^2*x^2)+-1//12*c*a^-4*arctan(a*x)^2+-1//180*c*a^-2*x^2+1//4*c*x^4*arctan(a*x)^2+-1//15*a*c*x^5*arctan(a*x)+-1//18*c*a^-1*x^3*arctan(a*x)+1//6*c*x*a^-3*arctan(a*x)+1//6*c*a^2*x^6*arctan(a*x)^2)
@test integrate(x^2*arctan(a*x)^2*(c+c*a^2*x^2), x) == :(1//30*c*x^3+-1//30*c*a^-3*arctan(a*x)+1//3*c*x^3*arctan(a*x)^2+1//30*c*x*a^-2+-4//15*c*a^-3*arctan(a*x)*log(2*(1+im*a*x)^-1)+-2//15*im*c*a^-3*arctan(a*x)^2+-2//15*im*c*a^-3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-2//15*c*a^-1*x^2*arctan(a*x)+-1//10*a*c*x^4*arctan(a*x)+1//5*c*a^2*x^5*arctan(a*x)^2)
@test integrate(x*arctan(a*x)^2*(c+c*a^2*x^2), x) == :(1//6*c*a^-2*log(1+a^2*x^2)+1//12*c*a^-2*(1+a^2*x^2)+-1//3*c*x*a^-1*arctan(a*x)+1//4*c*a^-2*(1+a^2*x^2)^2*arctan(a*x)^2+-1//6*c*x*a^-1*(1+a^2*x^2)*arctan(a*x))
@test integrate(arctan(a*x)^2*(c+c*a^2*x^2), x) == :(1//3*c*x+2//3*c*x*arctan(a*x)^2+-1//3*c*a^-1*(1+a^2*x^2)*arctan(a*x)+1//3*c*x*arctan(a*x)^2*(1+a^2*x^2)+2//3*im*c*a^-1*arctan(a*x)^2+2//3*im*c*a^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+4//3*c*a^-1*arctan(a*x)*log(2*(1+im*a*x)^-1))
@test integrate(x^-1*arctan(a*x)^2*(c+c*a^2*x^2), x) == :((1/2)*c*arctan(a*x)^2+(1/2)*c*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)+(1/2)*c*log(1+a^2*x^2)+-1//2*c*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+2*c*arctan(a*x)^2*arctanh(1+-2*(1+im*a*x)^-1)+im*c*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1)*arctan(a*x)+(1/2)*c*a^2*x^2*arctan(a*x)^2+-1*im*c*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-1*a*c*x*arctan(a*x))
@test integrate(x^-2*arctan(a*x)^2*(c+c*a^2*x^2), x) == :(-1*c*x^-1*arctan(a*x)^2+im*a*c*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+c*x*a^2*arctan(a*x)^2+-1*im*a*c*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+2*a*c*arctan(a*x)*log(2*(1+im*a*x)^-1)+2*a*c*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1))
@test integrate(x^-3*arctan(a*x)^2*(c+c*a^2*x^2), x) == :(c*a^2*log(x)+(1/2)*c*a^2*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)+-1//2*c*a^2*arctan(a*x)^2+-1//2*c*a^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1//2*c*a^2*log(1+a^2*x^2)+-1//2*c*x^-2*arctan(a*x)^2+-1*a*c*x^-1*arctan(a*x)+2*c*a^2*arctan(a*x)^2*arctanh(1+-2*(1+im*a*x)^-1)+im*c*a^2*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1)*arctan(a*x)+-1*im*c*a^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^-4*arctan(a*x)^2*(c+c*a^2*x^2), x) == :(-1//3*c*a^2*x^-1+-1//3*c*a^3*arctan(a*x)+-1//3*c*x^-3*arctan(a*x)^2+-1*c*a^2*x^-1*arctan(a*x)^2+-2//3*im*c*a^3*arctan(a*x)^2+-2//3*im*c*a^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-1//3*a*c*x^-2*arctan(a*x)+4//3*c*a^3*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1))
@test integrate(x^3*(c+c*a^2*x^2)^2*arctan(a*x)^2, x) == :(1//84*c^2*x^4+-5//504*a^-2*c^2*x^2+-2//63*a^-4*c^2*log(1+a^2*x^2)+-1//24*a^-4*c^2*arctan(a*x)^2+1//4*c^2*x^4*arctan(a*x)^2+1//168*a^2*c^2*x^6+-1//12*a*c^2*x^5*arctan(a*x)+-1//28*a^3*c^2*x^7*arctan(a*x)+-1//36*a^-1*c^2*x^3*arctan(a*x)+1//3*a^2*c^2*x^6*arctan(a*x)^2+1//8*a^4*c^2*x^8*arctan(a*x)^2+1//12*x*a^-3*c^2*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^2*arctan(a*x)^2, x) == :(17//630*c^2*x^3+-1//210*x*a^-2*c^2+1//3*c^2*x^3*arctan(a*x)^2+1//105*a^2*c^2*x^5+1//210*a^-3*c^2*arctan(a*x)+-16//105*a^-3*c^2*arctan(a*x)*log(2*(1+im*a*x)^-1)+-9//70*a*c^2*x^4*arctan(a*x)+-8//105*im*a^-3*c^2*arctan(a*x)^2+-8//105*im*a^-3*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-8//105*a^-1*c^2*x^2*arctan(a*x)+-1//21*a^3*c^2*x^6*arctan(a*x)+1//7*a^4*c^2*x^7*arctan(a*x)^2+2//5*a^2*c^2*x^5*arctan(a*x)^2)
@test integrate(x*(c+c*a^2*x^2)^2*arctan(a*x)^2, x) == :(1//60*a^-2*c^2*(1+a^2*x^2)^2+2//45*a^-2*c^2*(1+a^2*x^2)+4//45*a^-2*c^2*log(1+a^2*x^2)+-8//45*x*a^-1*c^2*arctan(a*x)+1//6*a^-2*c^2*(1+a^2*x^2)^3*arctan(a*x)^2+-4//45*x*a^-1*c^2*(1+a^2*x^2)*arctan(a*x)+-1//15*x*a^-1*c^2*(1+a^2*x^2)^2*arctan(a*x))
@test integrate((c+c*a^2*x^2)^2*arctan(a*x)^2, x) == :(11//30*x*c^2+1//30*a^2*c^2*x^3+8//15*x*c^2*arctan(a*x)^2+-4//15*a^-1*c^2*(1+a^2*x^2)*arctan(a*x)+-1//10*a^-1*c^2*(1+a^2*x^2)^2*arctan(a*x)+1//5*x*c^2*(1+a^2*x^2)^2*arctan(a*x)^2+4//15*x*c^2*arctan(a*x)^2*(1+a^2*x^2)+8//15*im*a^-1*c^2*arctan(a*x)^2+8//15*im*a^-1*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+16//15*a^-1*c^2*arctan(a*x)*log(2*(1+im*a*x)^-1))
@test integrate(x^-1*(c+c*a^2*x^2)^2*arctan(a*x)^2, x) == :((1/2)*c^2*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)+-1//2*c^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+2//3*c^2*log(1+a^2*x^2)+3//4*c^2*arctan(a*x)^2+2*c^2*arctan(a*x)^2*arctanh(1+-2*(1+im*a*x)^-1)+1//12*a^2*c^2*x^2+im*c^2*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1)*arctan(a*x)+a^2*c^2*x^2*arctan(a*x)^2+-1*im*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-3//2*a*x*c^2*arctan(a*x)+-1//6*a^3*c^2*x^3*arctan(a*x)+1//4*a^4*c^2*x^4*arctan(a*x)^2)
@test integrate(x^-2*(c+c*a^2*x^2)^2*arctan(a*x)^2, x) == :(-1*c^2*x^-1*arctan(a*x)^2+-1//3*a*c^2*arctan(a*x)+1//3*x*a^2*c^2+-1*im*a*c^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+2*a*c^2*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+2*x*a^2*c^2*arctan(a*x)^2+-1//3*a^3*c^2*x^2*arctan(a*x)+1//3*a^4*c^2*x^3*arctan(a*x)^2+2//3*im*a*c^2*arctan(a*x)^2+5//3*im*a*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+10//3*a*c^2*arctan(a*x)*log(2*(1+im*a*x)^-1))
@test integrate(x^-3*(c+c*a^2*x^2)^2*arctan(a*x)^2, x) == :(a^2*c^2*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)+a^2*c^2*log(x)+-1*a^2*c^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1//2*c^2*x^-2*arctan(a*x)^2+(1/2)*a^4*c^2*x^2*arctan(a*x)^2+-1*a*c^2*x^-1*arctan(a*x)+-1*x*a^3*c^2*arctan(a*x)+4*a^2*c^2*arctan(a*x)^2*arctanh(1+-2*(1+im*a*x)^-1)+-2*im*a^2*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x)+2*im*a^2*c^2*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^2*arctan(a*x)^2, x) == :(-1//3*a^2*c^2*x^-1+-1//3*a^3*c^2*arctan(a*x)+-1//3*c^2*x^-3*arctan(a*x)^2+im*a^3*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+x*a^4*c^2*arctan(a*x)^2+-2*a^2*c^2*x^-1*arctan(a*x)^2+2*a^3*c^2*arctan(a*x)*log(2*(1+im*a*x)^-1)+-5//3*im*a^3*c^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-2//3*im*a^3*c^2*arctan(a*x)^2+-1//3*a*c^2*x^-2*arctan(a*x)+10//3*a^3*c^2*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1))
@test integrate(x^3*(c+c*a^2*x^2)^3*arctan(a*x)^2, x) == :(53//6300*c^3*x^4+-107//12600*a^-2*c^3*x^2+-26//1575*a^-4*c^3*log(1+a^2*x^2)+-1//40*a^-4*c^3*arctan(a*x)^2+1//4*c^3*x^4*arctan(a*x)^2+1//360*a^4*c^3*x^8+71//7560*a^2*c^3*x^6+(1/2)*a^2*c^3*x^6*arctan(a*x)^2+-11//140*a^3*c^3*x^7*arctan(a*x)+-9//100*a*c^3*x^5*arctan(a*x)+-1//45*a^5*c^3*x^9*arctan(a*x)+-1//60*a^-1*c^3*x^3*arctan(a*x)+1//10*a^6*c^3*x^10*arctan(a*x)^2+1//20*x*a^-3*c^3*arctan(a*x)+3//8*a^4*c^3*x^8*arctan(a*x)^2)
@test integrate(x^2*(c+c*a^2*x^2)^3*arctan(a*x)^2, x) == :(239//11340*c^3*x^3+-47//3780*x*a^-2*c^3+1//3*c^3*x^3*arctan(a*x)^2+1//252*a^4*c^3*x^7+47//3780*a^-3*c^3*arctan(a*x)+59//3780*a^2*c^3*x^5+-89//630*a*c^3*x^4*arctan(a*x)+-32//315*a^-3*c^3*arctan(a*x)*log(2*(1+im*a*x)^-1)+-20//189*a^3*c^3*x^6*arctan(a*x)+-16//315*im*a^-3*c^3*arctan(a*x)^2+-16//315*im*a^-3*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-16//315*a^-1*c^3*x^2*arctan(a*x)+-1//36*a^5*c^3*x^8*arctan(a*x)+1//9*a^6*c^3*x^9*arctan(a*x)^2+3//5*a^2*c^3*x^5*arctan(a*x)^2+3//7*a^4*c^3*x^7*arctan(a*x)^2)
@test integrate(x*(c+c*a^2*x^2)^3*arctan(a*x)^2, x) == :(1//35*a^-2*c^3*(1+a^2*x^2)+1//168*a^-2*c^3*(1+a^2*x^2)^3+2//35*a^-2*c^3*log(1+a^2*x^2)+3//280*a^-2*c^3*(1+a^2*x^2)^2+-4//35*x*a^-1*c^3*arctan(a*x)+1//8*a^-2*c^3*(1+a^2*x^2)^4*arctan(a*x)^2+-3//70*x*a^-1*c^3*(1+a^2*x^2)^2*arctan(a*x)+-2//35*x*a^-1*c^3*(1+a^2*x^2)*arctan(a*x)+-1//28*x*a^-1*c^3*(1+a^2*x^2)^3*arctan(a*x))
@test integrate((c+c*a^2*x^2)^3*arctan(a*x)^2, x) == :(38//105*x*c^3+1//105*a^4*c^3*x^5+16//35*x*c^3*arctan(a*x)^2+19//315*a^2*c^3*x^3+-8//35*a^-1*c^3*(1+a^2*x^2)*arctan(a*x)+-3//35*a^-1*c^3*(1+a^2*x^2)^2*arctan(a*x)+-1//21*a^-1*c^3*(1+a^2*x^2)^3*arctan(a*x)+1//7*x*c^3*(1+a^2*x^2)^3*arctan(a*x)^2+6//35*x*c^3*(1+a^2*x^2)^2*arctan(a*x)^2+8//35*x*c^3*arctan(a*x)^2*(1+a^2*x^2)+16//35*im*a^-1*c^3*arctan(a*x)^2+16//35*im*a^-1*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+32//35*a^-1*c^3*arctan(a*x)*log(2*(1+im*a*x)^-1))
@test integrate(x^-1*(c+c*a^2*x^2)^3*arctan(a*x)^2, x) == :((1/2)*c^3*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)+-1//2*c^3*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+11//12*c^3*arctan(a*x)^2+34//45*c^3*log(1+a^2*x^2)+2*c^3*arctan(a*x)^2*arctanh(1+-2*(1+im*a*x)^-1)+1//60*a^4*c^3*x^4+29//180*a^2*c^3*x^2+im*c^3*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1)*arctan(a*x)+-1*im*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-11//6*a*x*c^3*arctan(a*x)+-7//18*a^3*c^3*x^3*arctan(a*x)+-1//15*a^5*c^3*x^5*arctan(a*x)+1//6*a^6*c^3*x^6*arctan(a*x)^2+3//2*a^2*c^3*x^2*arctan(a*x)^2+3//4*a^4*c^3*x^4*arctan(a*x)^2)
@test integrate(x^-2*(c+c*a^2*x^2)^3*arctan(a*x)^2, x) == :(-1*c^3*x^-1*arctan(a*x)^2+-7//10*a*c^3*arctan(a*x)+1//30*a^4*c^3*x^3+7//10*x*a^2*c^3+a^4*c^3*x^3*arctan(a*x)^2+-1*im*a*c^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+2*a*c^3*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+3*x*a^2*c^3*arctan(a*x)^2+-4//5*a^3*c^3*x^2*arctan(a*x)+-1//10*a^5*c^3*x^4*arctan(a*x)+1//5*a^6*c^3*x^5*arctan(a*x)^2+6//5*im*a*c^3*arctan(a*x)^2+11//5*im*a*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+22//5*a*c^3*arctan(a*x)*log(2*(1+im*a*x)^-1))
@test integrate(x^-3*(c+c*a^2*x^2)^3*arctan(a*x)^2, x) == :(a^2*c^3*log(x)+-3//2*a^2*c^3*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1//2*c^3*x^-2*arctan(a*x)^2+1//12*a^4*c^3*x^2+2//3*a^2*c^3*log(1+a^2*x^2)+3//2*a^2*c^3*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)+3//4*a^2*c^3*arctan(a*x)^2+-1*a*c^3*x^-1*arctan(a*x)+6*a^2*c^3*arctan(a*x)^2*arctanh(1+-2*(1+im*a*x)^-1)+-5//2*x*a^3*c^3*arctan(a*x)+-1//6*a^5*c^3*x^3*arctan(a*x)+1//4*a^6*c^3*x^4*arctan(a*x)^2+3//2*a^4*c^3*x^2*arctan(a*x)^2+-3*im*a^2*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x)+3*im*a^2*c^3*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^3*arctan(a*x)^2, x) == :(-2//3*a^3*c^3*arctan(a*x)+-1//3*a^2*c^3*x^-1+-1//3*c^3*x^-3*arctan(a*x)^2+1//3*x*a^4*c^3+-3*a^2*c^3*x^-1*arctan(a*x)^2+3*x*a^4*c^3*arctan(a*x)^2+-8//3*im*a^3*c^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-1//3*a*c^3*x^-2*arctan(a*x)+-1//3*a^5*c^3*x^2*arctan(a*x)+1//3*a^6*c^3*x^3*arctan(a*x)^2+8//3*im*a^3*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+16//3*a^3*c^3*arctan(a*x)*log(2*(1+im*a*x)^-1)+16//3*a^3*c^3*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1))
@test integrate(x^4*(c+c*a^2*x^2)^-1*arctan(a*x)^2, x) == :(-1//3*a^-5*c^-1*arctan(a*x)+1//3*x*a^-4*c^-1+1//3*a^-5*c^-1*arctan(a*x)^3+-1*x*a^-4*c^-1*arctan(a*x)^2+-8//3*a^-5*c^-1*arctan(a*x)*log(2*(1+im*a*x)^-1)+-4//3*im*a^-5*c^-1*arctan(a*x)^2+-4//3*im*a^-5*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-1//3*a^-3*c^-1*x^2*arctan(a*x)+1//3*a^-2*c^-1*x^3*arctan(a*x)^2)
@test integrate(x^3*(c+c*a^2*x^2)^-1*arctan(a*x)^2, x) == :((1/2)*a^-4*c^-1*arctan(a*x)^2+(1/2)*a^-4*c^-1*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+(1/2)*a^-4*c^-1*log(1+a^2*x^2)+a^-4*c^-1*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+(1/2)*a^-2*c^-1*x^2*arctan(a*x)^2+-1*x*a^-3*c^-1*arctan(a*x)+1//3*im*a^-4*c^-1*arctan(a*x)^3+im*a^-4*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-1*arctan(a*x)^2, x) == :(-1//3*a^-3*c^-1*arctan(a*x)^3+im*a^-3*c^-1*arctan(a*x)^2+im*a^-3*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+x*a^-2*c^-1*arctan(a*x)^2+2*a^-3*c^-1*arctan(a*x)*log(2*(1+im*a*x)^-1))
@test integrate(x*(c+c*a^2*x^2)^-1*arctan(a*x)^2, x) == :(-1//2*a^-2*c^-1*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1*a^-2*c^-1*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+-1//3*im*a^-2*c^-1*arctan(a*x)^3+-1*im*a^-2*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^2, x) == :(1//3*a^-1*c^-1*arctan(a*x)^3)
@test integrate(x^-1*(c+c*a^2*x^2)^-1*arctan(a*x)^2, x) == :((1/2)*c^-1*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+c^-1*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-1//3*im*c^-1*arctan(a*x)^3+-1*im*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^-1*arctan(a*x)^2, x) == :(-1*c^-1*x^-1*arctan(a*x)^2+-1//3*a*c^-1*arctan(a*x)^3+-1*im*a*c^-1*arctan(a*x)^2+-1*im*a*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+2*a*c^-1*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1))
@test integrate(x^-3*(c+c*a^2*x^2)^-1*arctan(a*x)^2, x) == :(a^2*c^-1*log(x)+-1//2*a^2*c^-1*arctan(a*x)^2+-1//2*a^2*c^-1*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-1//2*a^2*c^-1*log(1+a^2*x^2)+-1//2*c^-1*x^-2*arctan(a*x)^2+-1*a*c^-1*x^-1*arctan(a*x)+-1*a^2*c^-1*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+1//3*im*a^2*c^-1*arctan(a*x)^3+im*a^2*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^-1*arctan(a*x)^2, x) == :(-1//3*a^2*c^-1*x^-1+-1//3*a^3*c^-1*arctan(a*x)+-1//3*c^-1*x^-3*arctan(a*x)^2+1//3*a^3*c^-1*arctan(a*x)^3+a^2*c^-1*x^-1*arctan(a*x)^2+-8//3*a^3*c^-1*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-1//3*a*c^-1*x^-2*arctan(a*x)+4//3*im*a^3*c^-1*arctan(a*x)^2+4//3*im*a^3*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1))
@test integrate(x^3*(c+c*a^2*x^2)^-2*arctan(a*x)^2, x) == :(-1//2*a^-4*c^-2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1//4*a^-4*c^-2*(1+a^2*x^2)^-1+-1//4*a^-4*c^-2*arctan(a*x)^2+(1/2)*a^-4*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2+-1*a^-4*c^-2*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+-1//3*im*a^-4*c^-2*arctan(a*x)^3+-1*im*a^-4*c^-2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-1//2*x*a^-3*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^2, x) == :(1//4*a^-3*c^-2*arctan(a*x)+1//6*a^-3*c^-2*arctan(a*x)^3+-1//2*a^-3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+1//4*x*a^-2*c^-2*(1+a^2*x^2)^-1+-1//2*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^2, x) == :(1//4*a^-2*c^-2*(1+a^2*x^2)^-1+1//4*a^-2*c^-2*arctan(a*x)^2+-1//2*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2+(1/2)*x*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^2, x) == :(-1//4*x*c^-2*(1+a^2*x^2)^-1+-1//4*a^-1*c^-2*arctan(a*x)+1//6*a^-1*c^-2*arctan(a*x)^3+(1/2)*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2+(1/2)*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^-2*arctan(a*x)^2, x) == :((1/2)*c^-2*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-1//4*c^-2*(1+a^2*x^2)^-1+-1//4*c^-2*arctan(a*x)^2+c^-2*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+(1/2)*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2+-1//3*im*c^-2*arctan(a*x)^3+-1*im*c^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+-1//2*a*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^-2*arctan(a*x)^2, x) == :(-1*c^-2*x^-1*arctan(a*x)^2+-1//2*a*c^-2*arctan(a*x)^3+1//4*a*c^-2*arctan(a*x)+-1*im*a*c^-2*arctan(a*x)^2+-1*im*a*c^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+2*a*c^-2*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-1//2*a*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+1//4*x*a^2*c^-2*(1+a^2*x^2)^-1+-1//2*x*a^2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^-3*(c+c*a^2*x^2)^-2*arctan(a*x)^2, x) == :(a^2*c^-2*log(x)+-1*a^2*c^-2*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-1//2*a^2*c^-2*log(1+a^2*x^2)+-1//2*c^-2*x^-2*arctan(a*x)^2+-1//4*a^2*c^-2*arctan(a*x)^2+1//4*a^2*c^-2*(1+a^2*x^2)^-1+-1*a*c^-2*x^-1*arctan(a*x)+-2*a^2*c^-2*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-1//2*a^2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2+2//3*im*a^2*c^-2*arctan(a*x)^3+(1/2)*x*a^3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+2*im*a^2*c^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^-2*arctan(a*x)^2, x) == :(-7//12*a^3*c^-2*arctan(a*x)+-1//3*a^2*c^-2*x^-1+-1//3*c^-2*x^-3*arctan(a*x)^2+5//6*a^3*c^-2*arctan(a*x)^3+(1/2)*a^3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+2*a^2*c^-2*x^-1*arctan(a*x)^2+-14//3*a^3*c^-2*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-1//3*a*c^-2*x^-2*arctan(a*x)+-1//4*x*a^4*c^-2*(1+a^2*x^2)^-1+7//3*im*a^3*c^-2*arctan(a*x)^2+7//3*im*a^3*c^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+(1/2)*x*a^4*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^2, x) == :(-3//32*a^-4*c^-3*arctan(a*x)^2+-1//32*c^-3*x^4*(1+a^2*x^2)^-2+3//32*a^-4*c^-3*(1+a^2*x^2)^-1+1//4*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)^2+1//8*a^-1*c^-3*x^3*(1+a^2*x^2)^-2*arctan(a*x)+3//16*x*a^-3*c^-3*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^2, x) == :(-1//64*a^-3*c^-3*arctan(a*x)+1//24*a^-3*c^-3*arctan(a*x)^3+-1//8*a^-3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+-1//64*x*a^-2*c^-3*(1+a^2*x^2)^-1+1//8*a^-3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+1//32*x*a^-2*c^-3*(1+a^2*x^2)^-2+-1//4*x*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+1//8*x*a^-2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^2, x) == :(1//32*a^-2*c^-3*(1+a^2*x^2)^-2+3//32*a^-2*c^-3*(1+a^2*x^2)^-1+3//32*a^-2*c^-3*arctan(a*x)^2+-1//4*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+1//8*x*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+3//16*x*a^-1*c^-3*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^2, x) == :(-15//64*x*c^-3*(1+a^2*x^2)^-1+-15//64*a^-1*c^-3*arctan(a*x)+-1//32*x*c^-3*(1+a^2*x^2)^-2+1//8*a^-1*c^-3*arctan(a*x)^3+1//4*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+1//8*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+3//8*x*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2+3//8*a^-1*c^-3*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^-3*arctan(a*x)^2, x) == :((1/2)*c^-3*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-11//32*c^-3*(1+a^2*x^2)^-1+-11//32*c^-3*arctan(a*x)^2+-1//32*c^-3*(1+a^2*x^2)^-2+c^-3*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+(1/2)*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2+-1//3*im*c^-3*arctan(a*x)^3+1//4*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+-1*im*c^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+-11//16*a*x*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+-1//8*a*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^-3*arctan(a*x)^2, x) == :(-1*c^-3*x^-1*arctan(a*x)^2+-5//8*a*c^-3*arctan(a*x)^3+31//64*a*c^-3*arctan(a*x)+-1*im*a*c^-3*arctan(a*x)^2+-1*im*a*c^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+2*a*c^-3*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-7//8*a*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+-1//8*a*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+1//32*x*a^2*c^-3*(1+a^2*x^2)^-2+31//64*x*a^2*c^-3*(1+a^2*x^2)^-1+-7//8*x*a^2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2+-1//4*x*a^2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2)
@test integrate(x^-3*(c+c*a^2*x^2)^-3*arctan(a*x)^2, x) == :(a^2*c^-3*log(x)+-3//2*a^2*c^-3*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-1//2*a^2*c^-3*log(1+a^2*x^2)+-1//2*c^-3*x^-2*arctan(a*x)^2+1//32*a^2*c^-3*(1+a^2*x^2)^-2+3//32*a^2*c^-3*arctan(a*x)^2+19//32*a^2*c^-3*(1+a^2*x^2)^-1+im*a^2*c^-3*arctan(a*x)^3+-1*a*c^-3*x^-1*arctan(a*x)+-1*a^2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2+-3*a^2*c^-3*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-1//4*a^2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+3*im*a^2*c^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+1//8*x*a^3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+19//16*x*a^3*c^-3*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^-3*arctan(a*x)^2, x) == :(-205//192*a^3*c^-3*arctan(a*x)+-1//3*a^2*c^-3*x^-1+-1//3*c^-3*x^-3*arctan(a*x)^2+35//24*a^3*c^-3*arctan(a*x)^3+3*a^2*c^-3*x^-1*arctan(a*x)^2+-47//64*x*a^4*c^-3*(1+a^2*x^2)^-1+-20//3*a^3*c^-3*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-1//3*a*c^-3*x^-2*arctan(a*x)+-1//32*x*a^4*c^-3*(1+a^2*x^2)^-2+1//8*a^3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+10//3*im*a^3*c^-3*arctan(a*x)^2+10//3*im*a^3*c^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+11//8*a^3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+1//4*x*a^4*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+11//8*x*a^4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2, x) == :(-11//60*a^-4*(c+c*a^2*x^2)^(1/2)+-2//15*a^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//5*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//30*a^-4*c^-1*(c+c*a^2*x^2)^3//2+-1//10*a^-1*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//12*x*a^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//15*a^-2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-11//60*im*c*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+11//60*im*c*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-11//30*im*c*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2, x) == :(-1//6*a^-3*c^(1/2)*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//4*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//12*x*a^-2*(c+c*a^2*x^2)^(1/2)+1//12*a^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//6*a^-1*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//8*x*a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//4*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+1//4*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-1//4*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+1//4*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+1//4*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2, x) == :(1//3*a^-2*(c+c*a^2*x^2)^(1/2)+-1//3*x*a^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//3*a^-2*c^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-1//3*im*c*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+1//3*im*c*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2//3*im*c*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate((c+c*a^2*x^2)^(1/2)*arctan(a*x)^2, x) == :(a^-1*c^(1/2)*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+(1/2)*x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1*a^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-1*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+-1*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-1*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2, x) == :((c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-2*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+2*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-2*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+2*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+2*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+4*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2, x) == :(-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-2*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+2*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-4*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-2*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+2*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2, x) == :(-1*a^2*c^(1/2)*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1//2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1*a*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-1*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+-1*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+-1*im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2, x) == :(-1//3*a^2*x^-1*(c+c*a^2*x^2)^(1/2)+-1//3*a*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//3*c^-1*x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-2//3*c*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1//3*im*c*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+1//3*im*c*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^3*(c+c*a^2*x^2)^3//2*arctan(a*x)^2, x) == :(-17//1260*a^-4*(c+c*a^2*x^2)^3//2+-17//280*c*a^-4*(c+c*a^2*x^2)^(1/2)+1//105*a^-4*c^-1*(c+c*a^2*x^2)^5//2+-2//35*c*a^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+8//35*c*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-23//420*c*a^-1*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//21*a*c*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//7*c*a^2*x^6*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//35*c*a^-2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+3//56*c*x*a^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-17//280*im*a^-4*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+17//280*im*a^-4*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-17//140*im*a^-4*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^2*(c+c*a^2*x^2)^3//2*arctan(a*x)^2, x) == :(-41//360*a^-3*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//60*c*x^3*(c+c*a^2*x^2)^(1/2)+1//36*c*x*a^-2*(c+c*a^2*x^2)^(1/2)+7//24*c*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+31//360*c*a^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-19//180*c*a^-1*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//8*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-1//15*a*c*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//6*c*a^2*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//8*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+1//16*c*x*a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//8*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+1//8*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+1//8*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^3//2*arctan(a*x)^2, x) == :(1//30*a^-2*(c+c*a^2*x^2)^3//2+3//20*c*a^-2*(c+c*a^2*x^2)^(1/2)+-1//10*x*a^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)+1//5*a^-2*c^-1*(c+c*a^2*x^2)^5//2*arctan(a*x)^2+-3//20*c*x*a^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-3//20*im*a^-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3//20*im*a^-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3//10*im*a^-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate((c+c*a^2*x^2)^3//2*arctan(a*x)^2, x) == :(-1//6*a^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)+1//4*x*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+1//12*c*x*(c+c*a^2*x^2)^(1/2)+5//6*a^-1*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-3//4*c*a^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+3//8*c*x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-3//4*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+3//4*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-3//4*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-3//4*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+3//4*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)^2, x) == :(1//3*c*(c+c*a^2*x^2)^(1/2)+1//3*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+c*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-7//3*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1//3*a*c*x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+7//3*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+2*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+14//3*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-2*(c+c*a^2*x^2)^3//2*arctan(a*x)^2, x) == :(a*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-1*a*c*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1*c*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+(1/2)*c*x*a^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-3*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+3*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-4*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-3*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+3*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)^2, x) == :(-1*a^2*c^3//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+c*a^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//2*c*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1*a*c*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-3*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+3*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-3*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-2*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+3*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+4*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-4*(c+c*a^2*x^2)^3//2*arctan(a*x)^2, x) == :(-1//3*x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-1//3*c*a^2*x^-1*(c+c*a^2*x^2)^(1/2)+-1*c*a^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-2*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+2*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-1//3*a*c*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-14//3*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-7//3*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+7//3*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-2*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+2*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^5//2*arctan(a*x)^2, x) == :(-23//7560*a^-4*(c+c*a^2*x^2)^5//2+-115//4032*a^-4*c^2*(c+c*a^2*x^2)^(1/2)+-115//18144*c*a^-4*(c+c*a^2*x^2)^3//2+1//252*a^-4*c^-1*(c+c*a^2*x^2)^7//2+-2//63*a^-4*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+5//21*c^2*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-205//6048*a^-1*c^2*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-103//1512*a*c^2*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//36*a^3*c^2*x^7*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//9*a^4*c^2*x^8*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//63*a^-2*c^2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+19//63*a^2*c^2*x^6*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+47//1344*x*a^-3*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-115//4032*im*a^-4*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+115//4032*im*a^-4*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-115//2016*im*a^-4*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^2*(c+c*a^2*x^2)^5//2*arctan(a*x)^2, x) == :(-397//5040*a^-3*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+29//1680*c^2*x^3*(c+c*a^2*x^2)^(1/2)+1//168*a^2*c^2*x^5*(c+c*a^2*x^2)^(1/2)+43//4032*x*a^-2*c^2*(c+c*a^2*x^2)^(1/2)+59//192*c^2*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1373//20160*a^-3*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-737//10080*a^-1*c^2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-83//840*a*c^2*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5//64*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-1//28*a^3*c^2*x^6*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//8*a^4*c^2*x^7*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+5//64*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+5//128*x*a^-2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+17//48*a^2*c^2*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-5//64*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+5//64*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+5//64*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^5//2*arctan(a*x)^2, x) == :(1//105*a^-2*(c+c*a^2*x^2)^5//2+5//56*a^-2*c^2*(c+c*a^2*x^2)^(1/2)+5//252*c*a^-2*(c+c*a^2*x^2)^3//2+-1//21*x*a^-1*(c+c*a^2*x^2)^5//2*arctan(a*x)+1//7*a^-2*c^-1*(c+c*a^2*x^2)^7//2*arctan(a*x)^2+-5//56*x*a^-1*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5//84*c*x*a^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)+-5//56*im*a^-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+5//56*im*a^-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+5//28*im*a^-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate((c+c*a^2*x^2)^5//2*arctan(a*x)^2, x) == :(-1//15*a^-1*(c+c*a^2*x^2)^5//2*arctan(a*x)+1//6*x*(c+c*a^2*x^2)^5//2*arctan(a*x)^2+1//60*c*x*(c+c*a^2*x^2)^3//2+17//180*x*c^2*(c+c*a^2*x^2)^(1/2)+259//360*a^-1*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-5//8*a^-1*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5//36*c*a^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)+5//16*x*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+5//24*c*x*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-5//8*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+5//8*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-5//8*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-5//8*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+5//8*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^5//2*arctan(a*x)^2, x) == :(1//5*(c+c*a^2*x^2)^5//2*arctan(a*x)^2+1//30*c*(c+c*a^2*x^2)^3//2+29//60*c^2*(c+c*a^2*x^2)^(1/2)+c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//3*c*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-149//60*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-29//60*a*x*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//10*a*c*x*(c+c*a^2*x^2)^3//2*arctan(a*x)+149//60*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+2*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+149//30*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-2*(c+c*a^2*x^2)^5//2*arctan(a*x)^2, x) == :(11//6*a*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-1*c^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-7//4*a*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//6*a*c*(c+c*a^2*x^2)^3//2*arctan(a*x)+1//12*x*a^2*c^2*(c+c*a^2*x^2)^(1/2)+-15//4*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+1//4*c*x*a^2*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+7//8*x*a^2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+15//4*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-4*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-15//4*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-15//4*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+15//4*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^5//2*arctan(a*x)^2, x) == :(-1*a^2*c^5//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+1//3*a^2*c^2*(c+c*a^2*x^2)^(1/2)+2*a^2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//2*c^2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//3*c*a^2*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-1*a*c^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+5*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-1//3*x*a^3*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-13//3*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+13//3*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-5*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+5*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+26//3*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-4*(c+c*a^2*x^2)^5//2*arctan(a*x)^2, x) == :(a^3*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-1*a^3*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//3*c*x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-1//3*a^2*c^2*x^-1*(c+c*a^2*x^2)^(1/2)+(1/2)*x*a^4*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-5*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-2*a^2*c^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+5*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-1//3*a*c^2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-26//3*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-13//3*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+13//3*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-5*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-5*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+5*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2, x) == :(1//3*a^-4*c^-1*(c+c*a^2*x^2)^(1/2)+-2//3*a^-4*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-5//3*im*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1//3*x*a^-3*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//3*a^-2*c^-1*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+5//3*im*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-10//3*im*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2, x) == :(a^-3*c^-1//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-1*a^-3*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+(1/2)*x*a^-2*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+-1*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2, x) == :(a^-2*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-2*im*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+4*im*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate((c+c*a^2*x^2)^-1//2*arctan(a*x)^2, x) == :(-2*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+2*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-2*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-2*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+2*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2, x) == :(-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-2*im*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+2*im*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2, x) == :(-1*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-4*a*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-3*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2, x) == :(-1*a^2*c^-1//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+-1*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-1//2*c^-1*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-1*a*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+-1*im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2, x) == :(-1//3*a^2*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)+-1//3*c^-1*x^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-5//3*im*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-1//3*a*c^-1*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+2//3*a^2*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+5//3*im*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+10//3*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2, x) == :(-2*a^-4*c^-1*(c+c*a^2*x^2)^-1//2+a^-4*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+a^-4*c^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-2*x*a^-3*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-2*im*a^-4*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a^-4*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+4*im*a^-4*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2, x) == :(-2*a^-3*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+2*x*a^-2*c^-1*(c+c*a^2*x^2)^-1//2+-1*x*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-2*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+2*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-2*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-2*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+2*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2, x) == :(2*a^-2*c^-1*(c+c*a^2*x^2)^-1//2+-1*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+2*x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^2, x) == :(-2*x*c^-1*(c+c*a^2*x^2)^-1//2+x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+2*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2, x) == :(-2*c^-1*(c+c*a^2*x^2)^-1//2+c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-2*a*x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-2*im*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+2*im*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2, x) == :(-1*c^-2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-2*a*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+2*x*a^2*c^-1*(c+c*a^2*x^2)^-1//2+-1*x*a^2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-4*a*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^-3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2, x) == :(-1*a^2*c^-3//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+2*a^2*c^-1*(c+c*a^2*x^2)^-1//2+-1*a^2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1//2*c^-2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1*a*c^-2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-3*a^2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+2*x*a^3*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+3*a^2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+3*a^2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-3*im*a^2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+3*im*a^2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-4*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2, x) == :(-2*x*a^4*c^-1*(c+c*a^2*x^2)^-1//2+2*a^3*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-1//3*a^2*c^-2*x^-1*(c+c*a^2*x^2)^(1/2)+-1//3*c^-2*x^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+x*a^4*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1//3*a*c^-2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+5//3*a^2*c^-2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-11//3*im*a^3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+11//3*im*a^3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+22//3*a^3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^5*(c+c*a^2*x^2)^-5//2*arctan(a*x)^2, x) == :(-32//9*a^-6*c^-2*(c+c*a^2*x^2)^-1//2+2//27*a^-6*c^-1*(c+c*a^2*x^2)^-3//2+a^-6*c^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+5//3*a^-6*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-10//3*x*a^-5*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-2//9*a^-3*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)+1//3*a^-4*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+-2*im*a^-6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a^-6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+4*im*a^-6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^4*(c+c*a^2*x^2)^-5//2*arctan(a*x)^2, x) == :(-22//9*a^-5*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+2//27*a^-2*c^-1*x^3*(c+c*a^2*x^2)^-3//2+22//9*x*a^-4*c^-2*(c+c*a^2*x^2)^-1//2+-1*x*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-2*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+2*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-2//9*a^-3*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)+-1//3*a^-2*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+-2*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-2*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+2*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^2, x) == :(-2//27*a^-4*c^-1*(c+c*a^2*x^2)^-3//2+14//9*a^-4*c^-2*(c+c*a^2*x^2)^-1//2+-2//3*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1//3*a^-2*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+2//9*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)+4//3*x*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^2, x) == :(-2//27*c^-1*x^3*(c+c*a^2*x^2)^-3//2+-4//9*x*a^-2*c^-2*(c+c*a^2*x^2)^-1//2+1//3*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+4//9*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+2//9*a^-1*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^2, x) == :(2//27*a^-2*c^-1*(c+c*a^2*x^2)^-3//2+4//9*a^-2*c^-2*(c+c*a^2*x^2)^-1//2+-1//3*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+2//9*x*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+4//9*x*a^-1*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^2, x) == :(-40//27*x*c^-2*(c+c*a^2*x^2)^-1//2+-2//27*x*c^-1*(c+c*a^2*x^2)^-3//2+1//3*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+2//3*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+2//9*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+4//3*a^-1*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^-5//2*arctan(a*x)^2, x) == :(-22//9*c^-2*(c+c*a^2*x^2)^-1//2+-2//27*c^-1*(c+c*a^2*x^2)^-3//2+c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+1//3*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-22//9*a*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-2//9*a*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+-2*im*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+2*im*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^2, x) == :(-1*c^-3*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-10//3*a*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-2//9*a*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+2//27*x*a^2*c^-1*(c+c*a^2*x^2)^-3//2+94//27*x*a^2*c^-2*(c+c*a^2*x^2)^-1//2+-5//3*x*a^2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1//3*x*a^2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+-4*a*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-2*im*a*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+2*im*a*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x^3*arctan(a*x)^3*(c+c*a^2*x^2), x) == :(-1//12*c*a^-4*arctan(a*x)^3+-1//15*c*a^-4*arctan(a*x)+-1//60*c*a^-1*x^3+1//4*c*x^4*arctan(a*x)^3+1//15*c*x*a^-3+1//20*c*x^4*arctan(a*x)+-1//10*a*c*x^5*arctan(a*x)^2+-1//12*c*a^-1*x^3*arctan(a*x)^2+-1//60*c*a^-2*x^2*arctan(a*x)+1//4*c*x*a^-3*arctan(a*x)^2+1//6*c*a^2*x^6*arctan(a*x)^3+7//15*c*a^-4*arctan(a*x)*log(2*(1+im*a*x)^-1)+7//30*im*c*a^-4*arctan(a*x)^2+7//30*im*c*a^-4*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1))
@test integrate(x^2*arctan(a*x)^3*(c+c*a^2*x^2), x) == :(-1//5*c*a^-3*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1//20*c*a^-1*x^2+-1//20*c*a^-3*arctan(a*x)^2+1//3*c*x^3*arctan(a*x)^3+1//10*c*x^3*arctan(a*x)+-3//20*a*c*x^4*arctan(a*x)^2+-2//5*c*a^-3*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+-2//15*im*c*a^-3*arctan(a*x)^3+-1//5*c*a^-1*x^2*arctan(a*x)^2+1//5*c*a^2*x^5*arctan(a*x)^3+1//10*c*x*a^-2*arctan(a*x)+-2//5*im*c*a^-3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x*arctan(a*x)^3*(c+c*a^2*x^2), x) == :(-1//4*c*x*a^-1+-1*c*a^-2*arctan(a*x)*log(2*(1+im*a*x)^-1)+-1//2*im*c*a^-2*arctan(a*x)^2+-1//2*im*c*a^-2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-1//2*c*x*a^-1*arctan(a*x)^2+1//4*c*a^-2*(1+a^2*x^2)^2*arctan(a*x)^3+1//4*c*a^-2*(1+a^2*x^2)*arctan(a*x)+-1//4*c*x*a^-1*arctan(a*x)^2*(1+a^2*x^2))
@test integrate(arctan(a*x)^3*(c+c*a^2*x^2), x) == :(c*x*arctan(a*x)+c*a^-1*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1//2*c*a^-1*log(1+a^2*x^2)+2//3*c*x*arctan(a*x)^3+2*c*a^-1*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+-1//2*c*a^-1*arctan(a*x)^2*(1+a^2*x^2)+1//3*c*x*arctan(a*x)^3*(1+a^2*x^2)+2//3*im*c*a^-1*arctan(a*x)^3+2*im*c*a^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^-1*arctan(a*x)^3*(c+c*a^2*x^2), x) == :((1/2)*c*arctan(a*x)^3+-3*c*arctan(a*x)*log(2*(1+im*a*x)^-1)+2*c*arctan(a*x)^3*arctanh(1+-2*(1+im*a*x)^-1)+-3//2*im*c*arctan(a*x)^2+-3//2*im*c*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-3//2*c*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-3//4*im*c*Polylogarithms.polylog(4,-1+2*(1+im*a*x)^-1)+3//2*c*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)*arctan(a*x)+3//4*im*c*Polylogarithms.polylog(4,1+-2*(1+im*a*x)^-1)+(1/2)*c*a^2*x^2*arctan(a*x)^3+-3//2*im*c*arctan(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-3//2*a*c*x*arctan(a*x)^2+3//2*im*c*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1))
@test integrate(x^-2*arctan(a*x)^3*(c+c*a^2*x^2), x) == :(-1*c*x^-1*arctan(a*x)^3+3//2*a*c*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+3//2*a*c*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+c*x*a^2*arctan(a*x)^3+3*a*c*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+3*a*c*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-3*im*a*c*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+3*im*a*c*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^-3*arctan(a*x)^3*(c+c*a^2*x^2), x) == :(-1//2*c*a^2*arctan(a*x)^3+-1//2*c*x^-2*arctan(a*x)^3+2*c*a^2*arctan(a*x)^3*arctanh(1+-2*(1+im*a*x)^-1)+3*c*a^2*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-3//2*im*c*a^2*arctan(a*x)^2+-3//2*im*c*a^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-3//2*a*c*x^-1*arctan(a*x)^2+-3//2*c*a^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-3//4*im*c*a^2*Polylogarithms.polylog(4,-1+2*(1+im*a*x)^-1)+3//2*c*a^2*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)*arctan(a*x)+3//4*im*c*a^2*Polylogarithms.polylog(4,1+-2*(1+im*a*x)^-1)+-3//2*im*c*a^2*arctan(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+3//2*im*c*a^2*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1))
@test integrate(x^-4*arctan(a*x)^3*(c+c*a^2*x^2), x) == :(c*a^3*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+c*a^3*log(x)+-1//2*c*a^3*arctan(a*x)^2+-1//2*c*a^3*log(1+a^2*x^2)+-1//3*c*x^-3*arctan(a*x)^3+-1*c*a^2*x^-1*arctan(a*x)^3+-1*c*a^2*x^-1*arctan(a*x)+2*c*a^3*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-2//3*im*c*a^3*arctan(a*x)^3+-1//2*a*c*x^-2*arctan(a*x)^2+-2*im*c*a^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^2*arctan(a*x)^3, x) == :(-1//21*a^-4*c^2*arctan(a*x)+-1//24*a^-4*c^2*arctan(a*x)^3+-1//168*a^-1*c^2*x^3+-1//280*a*c^2*x^5+1//4*c^2*x^4*arctan(a*x)^3+1//21*x*a^-3*c^2+1//28*c^2*x^4*arctan(a*x)+-5//168*a^-2*c^2*x^2*arctan(a*x)+-3//56*a^3*c^2*x^7*arctan(a*x)^2+-1//8*a*c^2*x^5*arctan(a*x)^2+-1//24*a^-1*c^2*x^3*arctan(a*x)^2+1//3*a^2*c^2*x^6*arctan(a*x)^3+1//8*x*a^-3*c^2*arctan(a*x)^2+1//8*a^4*c^2*x^8*arctan(a*x)^3+1//56*a^2*c^2*x^6*arctan(a*x)+2//21*im*a^-4*c^2*arctan(a*x)^2+2//21*im*a^-4*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+4//21*a^-4*c^2*arctan(a*x)*log(2*(1+im*a*x)^-1))
@test integrate(x^2*(c+c*a^2*x^2)^2*arctan(a*x)^3, x) == :(-11//420*a^-1*c^2*x^2+-4//35*a^-3*c^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1//140*a*c^2*x^4+1//3*c^2*x^3*arctan(a*x)^3+1//30*a^-3*c^2*log(1+a^2*x^2)+1//140*a^-3*c^2*arctan(a*x)^2+17//210*c^2*x^3*arctan(a*x)+-27//140*a*c^2*x^4*arctan(a*x)^2+-8//35*a^-3*c^2*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+-8//105*im*a^-3*c^2*arctan(a*x)^3+-4//35*a^-1*c^2*x^2*arctan(a*x)^2+-1//14*a^3*c^2*x^6*arctan(a*x)^2+-1//70*x*a^-2*c^2*arctan(a*x)+1//7*a^4*c^2*x^7*arctan(a*x)^3+1//35*a^2*c^2*x^5*arctan(a*x)+2//5*a^2*c^2*x^5*arctan(a*x)^3+-8//35*im*a^-3*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^2*arctan(a*x)^3, x) == :(-11//60*x*a^-1*c^2+-1//60*a*c^2*x^3+-8//15*a^-2*c^2*arctan(a*x)*log(2*(1+im*a*x)^-1)+-4//15*im*a^-2*c^2*arctan(a*x)^2+-4//15*im*a^-2*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-4//15*x*a^-1*c^2*arctan(a*x)^2+1//6*a^-2*c^2*(1+a^2*x^2)^3*arctan(a*x)^3+1//20*a^-2*c^2*(1+a^2*x^2)^2*arctan(a*x)+2//15*a^-2*c^2*(1+a^2*x^2)*arctan(a*x)+-2//15*x*a^-1*c^2*arctan(a*x)^2*(1+a^2*x^2)+-1//10*x*a^-1*c^2*(1+a^2*x^2)^2*arctan(a*x)^2)
@test integrate((c+c*a^2*x^2)^2*arctan(a*x)^3, x) == :(x*c^2*arctan(a*x)+-1//2*a^-1*c^2*log(1+a^2*x^2)+-1//20*a^-1*c^2*(1+a^2*x^2)+4//5*a^-1*c^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+8//15*x*c^2*arctan(a*x)^3+-3//20*a^-1*c^2*(1+a^2*x^2)^2*arctan(a*x)^2+-2//5*a^-1*c^2*arctan(a*x)^2*(1+a^2*x^2)+1//5*x*c^2*(1+a^2*x^2)^2*arctan(a*x)^3+1//10*x*c^2*(1+a^2*x^2)*arctan(a*x)+4//15*x*c^2*arctan(a*x)^3*(1+a^2*x^2)+8//5*a^-1*c^2*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+8//15*im*a^-1*c^2*arctan(a*x)^3+8//5*im*a^-1*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^2*arctan(a*x)^3, x) == :(1//4*c^2*arctan(a*x)+3//4*c^2*arctan(a*x)^3+-4*c^2*arctan(a*x)*log(2*(1+im*a*x)^-1)+-2*im*c^2*arctan(a*x)^2+-2*im*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+2*c^2*arctan(a*x)^3*arctanh(1+-2*(1+im*a*x)^-1)+-3//2*c^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-3//4*im*c^2*Polylogarithms.polylog(4,-1+2*(1+im*a*x)^-1)+-1//4*a*x*c^2+3//2*c^2*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)*arctan(a*x)+3//4*im*c^2*Polylogarithms.polylog(4,1+-2*(1+im*a*x)^-1)+a^2*c^2*x^2*arctan(a*x)^3+-9//4*a*x*c^2*arctan(a*x)^2+-3//2*im*c^2*arctan(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-1//4*a^3*c^2*x^3*arctan(a*x)^2+1//4*a^2*c^2*x^2*arctan(a*x)+1//4*a^4*c^2*x^4*arctan(a*x)^3+3//2*im*c^2*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1))
@test integrate(x^-2*(c+c*a^2*x^2)^2*arctan(a*x)^3, x) == :(-1*c^2*x^-1*arctan(a*x)^3+-1//2*a*c^2*arctan(a*x)^2+-1//2*a*c^2*log(1+a^2*x^2)+3//2*a*c^2*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+5//2*a*c^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+x*a^2*c^2*arctan(a*x)+2*x*a^2*c^2*arctan(a*x)^3+3*a*c^2*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+5*a*c^2*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+-1//2*a^3*c^2*x^2*arctan(a*x)^2+1//3*a^4*c^2*x^3*arctan(a*x)^3+2//3*im*a*c^2*arctan(a*x)^3+-3*im*a*c^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+5*im*a*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^2*arctan(a*x)^3, x) == :(-1//2*c^2*x^-2*arctan(a*x)^3+(1/2)*a^4*c^2*x^2*arctan(a*x)^3+-3*im*a^2*c^2*arctan(a*x)^2+-3*a^2*c^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-3*a^2*c^2*arctan(a*x)*log(2*(1+im*a*x)^-1)+3*a^2*c^2*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)*arctan(a*x)+3*a^2*c^2*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+4*a^2*c^2*arctan(a*x)^3*arctanh(1+-2*(1+im*a*x)^-1)+-3//2*im*a^2*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-3//2*im*a^2*c^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-3//2*im*a^2*c^2*Polylogarithms.polylog(4,-1+2*(1+im*a*x)^-1)+-3//2*a*c^2*x^-1*arctan(a*x)^2+-3//2*x*a^3*c^2*arctan(a*x)^2+3//2*im*a^2*c^2*Polylogarithms.polylog(4,1+-2*(1+im*a*x)^-1)+-3*im*a^2*c^2*arctan(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+3*im*a^2*c^2*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1))
@test integrate(x^-4*(c+c*a^2*x^2)^2*arctan(a*x)^3, x) == :(a^3*c^2*log(x)+-1//2*a^3*c^2*arctan(a*x)^2+-1//2*a^3*c^2*log(1+a^2*x^2)+-1//3*c^2*x^-3*arctan(a*x)^3+3//2*a^3*c^2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+5//2*a^3*c^2*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+x*a^4*c^2*arctan(a*x)^3+-1*a^2*c^2*x^-1*arctan(a*x)+-2*a^2*c^2*x^-1*arctan(a*x)^3+3*a^3*c^2*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+5*a^3*c^2*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-2//3*im*a^3*c^2*arctan(a*x)^3+-1//2*a*c^2*x^-2*arctan(a*x)^2+-5*im*a^3*c^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+3*im*a^3*c^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^3*arctan(a*x)^3, x) == :(-389//12600*a^-4*c^3*arctan(a*x)+-17//9450*a^-1*c^3*x^3+-1//40*a^-4*c^3*arctan(a*x)^3+-1//252*a*c^3*x^5+-1//840*a^3*c^3*x^7+1//4*c^3*x^4*arctan(a*x)^3+53//2100*c^3*x^4*arctan(a*x)+389//12600*x*a^-3*c^3+(1/2)*a^2*c^3*x^6*arctan(a*x)^3+-107//4200*a^-2*c^3*x^2*arctan(a*x)+-33//280*a^3*c^3*x^7*arctan(a*x)^2+-27//200*a*c^3*x^5*arctan(a*x)^2+-1//30*a^5*c^3*x^9*arctan(a*x)^2+-1//40*a^-1*c^3*x^3*arctan(a*x)^2+1//10*a^6*c^3*x^10*arctan(a*x)^3+1//120*a^4*c^3*x^8*arctan(a*x)+3//8*a^4*c^3*x^8*arctan(a*x)^3+3//40*x*a^-3*c^3*arctan(a*x)^2+26//525*im*a^-4*c^3*arctan(a*x)^2+26//525*im*a^-4*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+52//525*a^-4*c^3*arctan(a*x)*log(2*(1+im*a*x)^-1)+71//2520*a^2*c^3*x^6*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^3*arctan(a*x)^3, x) == :(-107//7560*a^-1*c^3*x^2+-11//1260*a*c^3*x^4+-8//105*a^-3*c^3*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1//504*a^3*c^3*x^6+1//3*c^3*x^3*arctan(a*x)^3+31//945*a^-3*c^3*log(1+a^2*x^2)+47//2520*a^-3*c^3*arctan(a*x)^2+239//3780*c^3*x^3*arctan(a*x)+-89//420*a*c^3*x^4*arctan(a*x)^2+-47//1260*x*a^-2*c^3*arctan(a*x)+-16//105*a^-3*c^3*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+-16//315*im*a^-3*c^3*arctan(a*x)^3+-10//63*a^3*c^3*x^6*arctan(a*x)^2+-8//105*a^-1*c^3*x^2*arctan(a*x)^2+-1//24*a^5*c^3*x^8*arctan(a*x)^2+1//9*a^6*c^3*x^9*arctan(a*x)^3+1//84*a^4*c^3*x^7*arctan(a*x)+3//5*a^2*c^3*x^5*arctan(a*x)^3+3//7*a^4*c^3*x^7*arctan(a*x)^3+59//1260*a^2*c^3*x^5*arctan(a*x)+-16//105*im*a^-3*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^3*arctan(a*x)^3, x) == :(-19//140*x*a^-1*c^3+-19//840*a*c^3*x^3+-1//280*a^3*c^3*x^5+-12//35*a^-2*c^3*arctan(a*x)*log(2*(1+im*a*x)^-1)+-6//35*im*a^-2*c^3*arctan(a*x)^2+-6//35*im*a^-2*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-6//35*x*a^-1*c^3*arctan(a*x)^2+1//8*a^-2*c^3*(1+a^2*x^2)^4*arctan(a*x)^3+1//56*a^-2*c^3*(1+a^2*x^2)^3*arctan(a*x)+3//35*a^-2*c^3*(1+a^2*x^2)*arctan(a*x)+9//280*a^-2*c^3*(1+a^2*x^2)^2*arctan(a*x)+-9//140*x*a^-1*c^3*(1+a^2*x^2)^2*arctan(a*x)^2+-3//35*x*a^-1*c^3*arctan(a*x)^2*(1+a^2*x^2)+-3//56*x*a^-1*c^3*(1+a^2*x^2)^3*arctan(a*x)^2)
@test integrate((c+c*a^2*x^2)^3*arctan(a*x)^3, x) == :(-13//210*a^-1*c^3*(1+a^2*x^2)+-7//15*a^-1*c^3*log(1+a^2*x^2)+-1//140*a^-1*c^3*(1+a^2*x^2)^2+14//15*x*c^3*arctan(a*x)+16//35*x*c^3*arctan(a*x)^3+24//35*a^-1*c^3*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-12//35*a^-1*c^3*arctan(a*x)^2*(1+a^2*x^2)+-9//70*a^-1*c^3*(1+a^2*x^2)^2*arctan(a*x)^2+-1//14*a^-1*c^3*(1+a^2*x^2)^3*arctan(a*x)^2+1//7*x*c^3*(1+a^2*x^2)^3*arctan(a*x)^3+1//35*x*c^3*(1+a^2*x^2)^2*arctan(a*x)+6//35*x*c^3*(1+a^2*x^2)^2*arctan(a*x)^3+8//35*x*c^3*arctan(a*x)^3*(1+a^2*x^2)+13//105*x*c^3*(1+a^2*x^2)*arctan(a*x)+16//35*im*a^-1*c^3*arctan(a*x)^3+48//35*a^-1*c^3*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+48//35*im*a^-1*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^-1*(c+c*a^2*x^2)^3*arctan(a*x)^3, x) == :(11//12*c^3*arctan(a*x)^3+13//30*c^3*arctan(a*x)+2*c^3*arctan(a*x)^3*arctanh(1+-2*(1+im*a*x)^-1)+-68//15*c^3*arctan(a*x)*log(2*(1+im*a*x)^-1)+-34//15*im*c^3*arctan(a*x)^2+-34//15*im*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-13//30*a*x*c^3+-3//2*c^3*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-3//4*im*c^3*Polylogarithms.polylog(4,-1+2*(1+im*a*x)^-1)+-1//60*a^3*c^3*x^3+3//2*c^3*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)*arctan(a*x)+3//4*im*c^3*Polylogarithms.polylog(4,1+-2*(1+im*a*x)^-1)+-11//4*a*x*c^3*arctan(a*x)^2+-7//12*a^3*c^3*x^3*arctan(a*x)^2+-3//2*im*c^3*arctan(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-1//10*a^5*c^3*x^5*arctan(a*x)^2+1//6*a^6*c^3*x^6*arctan(a*x)^3+1//20*a^4*c^3*x^4*arctan(a*x)+3//2*im*c^3*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1)+3//2*a^2*c^3*x^2*arctan(a*x)^3+3//4*a^4*c^3*x^4*arctan(a*x)^3+29//60*a^2*c^3*x^2*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^3*arctan(a*x)^3, x) == :(-1*a*c^3*log(1+a^2*x^2)+-1*c^3*x^-1*arctan(a*x)^3+-21//20*a*c^3*arctan(a*x)^2+-1//20*a^3*c^3*x^2+3//2*a*c^3*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+33//10*a*c^3*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+a^4*c^3*x^3*arctan(a*x)^3+3*a*c^3*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+3*x*a^2*c^3*arctan(a*x)^3+-6//5*a^3*c^3*x^2*arctan(a*x)^2+-3//20*a^5*c^3*x^4*arctan(a*x)^2+1//5*a^6*c^3*x^5*arctan(a*x)^3+1//10*a^4*c^3*x^3*arctan(a*x)+6//5*im*a*c^3*arctan(a*x)^3+21//10*x*a^2*c^3*arctan(a*x)+33//5*a*c^3*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+-3*im*a*c^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+33//5*im*a*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^3*arctan(a*x)^3, x) == :(-1//2*c^3*x^-2*arctan(a*x)^3+-1//4*x*a^3*c^3+1//4*a^2*c^3*arctan(a*x)+3//4*a^2*c^3*arctan(a*x)^3+-7*a^2*c^3*arctan(a*x)*log(2*(1+im*a*x)^-1)+-5*im*a^2*c^3*arctan(a*x)^2+3*a^2*c^3*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+6*a^2*c^3*arctan(a*x)^3*arctanh(1+-2*(1+im*a*x)^-1)+-15//4*x*a^3*c^3*arctan(a*x)^2+-9//2*a^2*c^3*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-9//4*im*a^2*c^3*Polylogarithms.polylog(4,-1+2*(1+im*a*x)^-1)+-7//2*im*a^2*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-3//2*im*a^2*c^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-3//2*a*c^3*x^-1*arctan(a*x)^2+-1//4*a^5*c^3*x^3*arctan(a*x)^2+1//4*a^4*c^3*x^2*arctan(a*x)+1//4*a^6*c^3*x^4*arctan(a*x)^3+3//2*a^4*c^3*x^2*arctan(a*x)^3+9//2*a^2*c^3*Polylogarithms.polylog(3,-1+2*(1+im*a*x)^-1)*arctan(a*x)+9//4*im*a^2*c^3*Polylogarithms.polylog(4,1+-2*(1+im*a*x)^-1)+-9//2*im*a^2*c^3*arctan(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+9//2*im*a^2*c^3*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+im*a*x)^-1))
@test integrate(x^-4*(c+c*a^2*x^2)^3*arctan(a*x)^3, x) == :(a^3*c^3*log(x)+-1*a^3*c^3*arctan(a*x)^2+-1*a^3*c^3*log(1+a^2*x^2)+4*a^3*c^3*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+4*a^3*c^3*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-1//3*c^3*x^-3*arctan(a*x)^3+x*a^4*c^3*arctan(a*x)+-1*a^2*c^3*x^-1*arctan(a*x)+-3*a^2*c^3*x^-1*arctan(a*x)^3+3*x*a^4*c^3*arctan(a*x)^3+8*a^3*c^3*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+8*a^3*c^3*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-1//2*a*c^3*x^-2*arctan(a*x)^2+-1//2*a^5*c^3*x^2*arctan(a*x)^2+1//3*a^6*c^3*x^3*arctan(a*x)^3+-8*im*a^3*c^3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+8*im*a^3*c^3*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^4*(c+c*a^2*x^2)^-1*arctan(a*x)^3, x) == :(-2*a^-5*c^-1*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+-1//2*a^-5*c^-1*arctan(a*x)^2+-1//2*a^-5*c^-1*log(1+a^2*x^2)+1//4*a^-5*c^-1*arctan(a*x)^4+x*a^-4*c^-1*arctan(a*x)+-1*x*a^-4*c^-1*arctan(a*x)^3+-4*a^-5*c^-1*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+-4//3*im*a^-5*c^-1*arctan(a*x)^3+-1//2*a^-3*c^-1*x^2*arctan(a*x)^2+1//3*a^-2*c^-1*x^3*arctan(a*x)^3+-4*im*a^-5*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-1*arctan(a*x)^3, x) == :((1/2)*a^-4*c^-1*arctan(a*x)^3+a^-4*c^-1*arctan(a*x)^3*log(2*(1+im*a*x)^-1)+(1/2)*a^-2*c^-1*x^2*arctan(a*x)^3+-3*a^-4*c^-1*arctan(a*x)*log(2*(1+im*a*x)^-1)+-3//2*im*a^-4*c^-1*arctan(a*x)^2+-3//2*im*a^-4*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-3//2*x*a^-3*c^-1*arctan(a*x)^2+-3//4*im*a^-4*c^-1*Polylogarithms.polylog(4,1+-2*(1+im*a*x)^-1)+1//4*im*a^-4*c^-1*arctan(a*x)^4+3//2*a^-4*c^-1*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)*arctan(a*x)+3//2*im*a^-4*c^-1*arctan(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1))
@test integrate(x^2*(c+c*a^2*x^2)^-1*arctan(a*x)^3, x) == :(-1//4*a^-3*c^-1*arctan(a*x)^4+3//2*a^-3*c^-1*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)+im*a^-3*c^-1*arctan(a*x)^3+x*a^-2*c^-1*arctan(a*x)^3+3*a^-3*c^-1*arctan(a*x)^2*log(2*(1+im*a*x)^-1)+3*im*a^-3*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-1*arctan(a*x)^3, x) == :(-1*a^-2*c^-1*arctan(a*x)^3*log(2*(1+im*a*x)^-1)+-3//2*a^-2*c^-1*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-1//4*im*a^-2*c^-1*arctan(a*x)^4+3//4*im*a^-2*c^-1*Polylogarithms.polylog(4,1+-2*(1+im*a*x)^-1)+-3//2*im*a^-2*c^-1*arctan(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^3, x) == :(1//4*a^-1*c^-1*arctan(a*x)^4)
@test integrate(x^-1*(c+c*a^2*x^2)^-1*arctan(a*x)^3, x) == :(c^-1*arctan(a*x)^3*log(2+-2*(1+-1*im*a*x)^-1)+-1//4*im*c^-1*arctan(a*x)^4+3//2*c^-1*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+3//4*im*c^-1*Polylogarithms.polylog(4,-1+2*(1+-1*im*a*x)^-1)+-3//2*im*c^-1*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1))
@test integrate(x^-2*(c+c*a^2*x^2)^-1*arctan(a*x)^3, x) == :(-1*c^-1*x^-1*arctan(a*x)^3+-1//4*a*c^-1*arctan(a*x)^4+3//2*a*c^-1*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-1*im*a*c^-1*arctan(a*x)^3+3*a*c^-1*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-3*im*a*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^-1*arctan(a*x)^3, x) == :(-1//2*a^2*c^-1*arctan(a*x)^3+-1//2*c^-1*x^-2*arctan(a*x)^3+-1*a^2*c^-1*arctan(a*x)^3*log(2+-2*(1+-1*im*a*x)^-1)+3*a^2*c^-1*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-3//2*im*a^2*c^-1*arctan(a*x)^2+-3//2*im*a^2*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-3//2*a*c^-1*x^-1*arctan(a*x)^2+-3//2*a^2*c^-1*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+-3//4*im*a^2*c^-1*Polylogarithms.polylog(4,-1+2*(1+-1*im*a*x)^-1)+1//4*im*a^2*c^-1*arctan(a*x)^4+3//2*im*a^2*c^-1*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1))
@test integrate(x^-4*(c+c*a^2*x^2)^-1*arctan(a*x)^3, x) == :(a^3*c^-1*log(x)+-2*a^3*c^-1*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-1//2*a^3*c^-1*arctan(a*x)^2+-1//2*a^3*c^-1*log(1+a^2*x^2)+-1//3*c^-1*x^-3*arctan(a*x)^3+1//4*a^3*c^-1*arctan(a*x)^4+a^2*c^-1*x^-1*arctan(a*x)^3+-1*a^2*c^-1*x^-1*arctan(a*x)+-4*a^3*c^-1*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-1//2*a*c^-1*x^-2*arctan(a*x)^2+4//3*im*a^3*c^-1*arctan(a*x)^3+4*im*a^3*c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-2*arctan(a*x)^3, x) == :(-1//4*a^-4*c^-2*arctan(a*x)^3+3//8*a^-4*c^-2*arctan(a*x)+(1/2)*a^-4*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3+-1*a^-4*c^-2*arctan(a*x)^3*log(2*(1+im*a*x)^-1)+-3//2*a^-4*c^-2*Polylogarithms.polylog(3,1+-2*(1+im*a*x)^-1)*arctan(a*x)+-3//4*a^-4*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+-1//4*im*a^-4*c^-2*arctan(a*x)^4+3//4*im*a^-4*c^-2*Polylogarithms.polylog(4,1+-2*(1+im*a*x)^-1)+3//8*x*a^-3*c^-2*(1+a^2*x^2)^-1+-3//2*im*a^-4*c^-2*arctan(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+im*a*x)^-1)+-3//4*x*a^-3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^3, x) == :(1//8*a^-3*c^-2*arctan(a*x)^4+3//8*a^-3*c^-2*(1+a^2*x^2)^-1+3//8*a^-3*c^-2*arctan(a*x)^2+-3//4*a^-3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2+-1//2*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3+3//4*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^3, x) == :(-3//8*a^-2*c^-2*arctan(a*x)+1//4*a^-2*c^-2*arctan(a*x)^3+-3//8*x*a^-1*c^-2*(1+a^2*x^2)^-1+-1//2*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3+3//4*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+3//4*x*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^3, x) == :(-3//8*a^-1*c^-2*(1+a^2*x^2)^-1+-3//8*a^-1*c^-2*arctan(a*x)^2+1//8*a^-1*c^-2*arctan(a*x)^4+(1/2)*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3+-3//4*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+3//4*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^-1*(c+c*a^2*x^2)^-2*arctan(a*x)^3, x) == :(-1//4*c^-2*arctan(a*x)^3+3//8*c^-2*arctan(a*x)+c^-2*arctan(a*x)^3*log(2+-2*(1+-1*im*a*x)^-1)+(1/2)*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3+-3//4*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+-1//4*im*c^-2*arctan(a*x)^4+3//2*c^-2*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+3//4*im*c^-2*Polylogarithms.polylog(4,-1+2*(1+-1*im*a*x)^-1)+-3//2*im*c^-2*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+3//8*a*x*c^-2*(1+a^2*x^2)^-1+-3//4*a*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^-2*(c+c*a^2*x^2)^-2*arctan(a*x)^3, x) == :(-1*c^-2*x^-1*arctan(a*x)^3+-3//8*a*c^-2*arctan(a*x)^4+3//2*a*c^-2*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+3//8*a*c^-2*(1+a^2*x^2)^-1+3//8*a*c^-2*arctan(a*x)^2+-1*im*a*c^-2*arctan(a*x)^3+3*a*c^-2*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-3//4*a*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2+-3*im*a*c^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+-1//2*x*a^2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3+3//4*x*a^2*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^-2*arctan(a*x)^3, x) == :(-3//8*a^2*c^-2*arctan(a*x)+-1//2*c^-2*x^-2*arctan(a*x)^3+-1//4*a^2*c^-2*arctan(a*x)^3+(1/2)*im*a^2*c^-2*arctan(a*x)^4+-3*a^2*c^-2*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+-2*a^2*c^-2*arctan(a*x)^3*log(2+-2*(1+-1*im*a*x)^-1)+3*a^2*c^-2*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-3//2*im*a^2*c^-2*arctan(a*x)^2+-3//2*im*a^2*c^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-3//2*im*a^2*c^-2*Polylogarithms.polylog(4,-1+2*(1+-1*im*a*x)^-1)+-3//2*a*c^-2*x^-1*arctan(a*x)^2+-3//8*x*a^3*c^-2*(1+a^2*x^2)^-1+-1//2*a^2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3+3//4*a^2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)+3*im*a^2*c^-2*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+3//4*x*a^3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^-4*(c+c*a^2*x^2)^-2*arctan(a*x)^3, x) == :(a^3*c^-2*log(x)+-7//2*a^3*c^-2*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-7//8*a^3*c^-2*arctan(a*x)^2+-3//8*a^3*c^-2*(1+a^2*x^2)^-1+-1//2*a^3*c^-2*log(1+a^2*x^2)+-1//3*c^-2*x^-3*arctan(a*x)^3+5//8*a^3*c^-2*arctan(a*x)^4+-1*a^2*c^-2*x^-1*arctan(a*x)+-7*a^3*c^-2*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+2*a^2*c^-2*x^-1*arctan(a*x)^3+-1//2*a*c^-2*x^-2*arctan(a*x)^2+3//4*a^3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^2+7//3*im*a^3*c^-2*arctan(a*x)^3+(1/2)*x*a^4*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3+7*im*a^3*c^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+-3//4*x*a^4*c^-2*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^3, x) == :(-27//256*a^-4*c^-3*arctan(a*x)+-3//32*a^-4*c^-3*arctan(a*x)^3+-45//256*x*a^-3*c^-3*(1+a^2*x^2)^-1+-3//32*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)+-3//128*a^-1*c^-3*x^3*(1+a^2*x^2)^-2+1//4*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)^3+9//32*a^-4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+3//16*a^-1*c^-3*x^3*(1+a^2*x^2)^-2*arctan(a*x)^2+9//32*x*a^-3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^3, x) == :(-3//128*a^-3*c^-3*(1+a^2*x^2)^-1+-3//128*a^-3*c^-3*arctan(a*x)^2+1//32*a^-3*c^-3*arctan(a*x)^4+3//128*a^-3*c^-3*(1+a^2*x^2)^-2+-3//16*a^-3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+3//16*a^-3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2+-3//64*x*a^-2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+-1//4*x*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3+1//8*x*a^-2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3+3//32*x*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x))
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^3, x) == :(-45//256*a^-2*c^-3*arctan(a*x)+3//32*a^-2*c^-3*arctan(a*x)^3+-45//256*x*a^-1*c^-3*(1+a^2*x^2)^-1+-3//128*x*a^-1*c^-3*(1+a^2*x^2)^-2+-1//4*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3+3//32*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+9//32*a^-2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+3//16*x*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+9//32*x*a^-1*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^3, x) == :(-45//128*a^-1*c^-3*(1+a^2*x^2)^-1+-45//128*a^-1*c^-3*arctan(a*x)^2+-3//128*a^-1*c^-3*(1+a^2*x^2)^-2+3//32*a^-1*c^-3*arctan(a*x)^4+-45//64*x*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+-3//32*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+1//4*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3+3//8*x*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3+3//16*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+9//16*a^-1*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^-1*(c+c*a^2*x^2)^-3*arctan(a*x)^3, x) == :(-11//32*c^-3*arctan(a*x)^3+141//256*c^-3*arctan(a*x)+c^-3*arctan(a*x)^3*log(2+-2*(1+-1*im*a*x)^-1)+(1/2)*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3+-33//32*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+-3//32*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+-1//4*im*c^-3*arctan(a*x)^4+1//4*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3+3//2*c^-3*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+3//4*im*c^-3*Polylogarithms.polylog(4,-1+2*(1+-1*im*a*x)^-1)+-3//2*im*c^-3*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+3//128*a*x*c^-3*(1+a^2*x^2)^-2+141//256*a*x*c^-3*(1+a^2*x^2)^-1+-33//32*a*x*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2+-3//16*a*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2)
@test integrate(x^-2*(c+c*a^2*x^2)^-3*arctan(a*x)^3, x) == :(-1*c^-3*x^-1*arctan(a*x)^3+-15//32*a*c^-3*arctan(a*x)^4+3//2*a*c^-3*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+3//128*a*c^-3*(1+a^2*x^2)^-2+93//128*a*c^-3*(1+a^2*x^2)^-1+93//128*a*c^-3*arctan(a*x)^2+-1*im*a*c^-3*arctan(a*x)^3+3*a*c^-3*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+-21//16*a*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2+-3//16*a*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+-3*im*a*c^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+-7//8*x*a^2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3+-1//4*x*a^2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3+3//32*x*a^2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+93//64*x*a^2*c^-3*(1+a^2*x^2)^-1*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^-3*arctan(a*x)^3, x) == :(-237//256*a^2*c^-3*arctan(a*x)+-1//2*c^-3*x^-2*arctan(a*x)^3+3//32*a^2*c^-3*arctan(a*x)^3+-1*a^2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3+-3*a^2*c^-3*arctan(a*x)^3*log(2+-2*(1+-1*im*a*x)^-1)+3*a^2*c^-3*arctan(a*x)*log(2+-2*(1+-1*im*a*x)^-1)+-237//256*x*a^3*c^-3*(1+a^2*x^2)^-1+-9//2*a^2*c^-3*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+-9//4*im*a^2*c^-3*Polylogarithms.polylog(4,-1+2*(1+-1*im*a*x)^-1)+-3//2*im*a^2*c^-3*arctan(a*x)^2+-3//2*im*a^2*c^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+-3//2*a*c^-3*x^-1*arctan(a*x)^2+-3//128*x*a^3*c^-3*(1+a^2*x^2)^-2+-1//4*a^2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3+3//4*im*a^2*c^-3*arctan(a*x)^4+3//32*a^2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+57//32*a^2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+3//16*x*a^3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+9//2*im*a^2*c^-3*arctan(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)+57//32*x*a^3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2)
@test integrate(x^-4*(c+c*a^2*x^2)^-3*arctan(a*x)^3, x) == :(a^3*c^-3*log(x)+-5*a^3*c^-3*Polylogarithms.polylog(3,-1+2*(1+-1*im*a*x)^-1)+-205//128*a^3*c^-3*arctan(a*x)^2+-141//128*a^3*c^-3*(1+a^2*x^2)^-1+-3//128*a^3*c^-3*(1+a^2*x^2)^-2+-1//2*a^3*c^-3*log(1+a^2*x^2)+-1//3*c^-3*x^-3*arctan(a*x)^3+35//32*a^3*c^-3*arctan(a*x)^4+-1*a^2*c^-3*x^-1*arctan(a*x)+-10*a^3*c^-3*arctan(a*x)^2*log(2+-2*(1+-1*im*a*x)^-1)+3*a^2*c^-3*x^-1*arctan(a*x)^3+-1//2*a*c^-3*x^-2*arctan(a*x)^2+3//16*a^3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^2+10//3*im*a^3*c^-3*arctan(a*x)^3+33//16*a^3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^2+10*im*a^3*c^-3*Polylogarithms.polylog(2,-1+2*(1+-1*im*a*x)^-1)*arctan(a*x)+-141//64*x*a^4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)+-3//32*x*a^4*c^-3*(1+a^2*x^2)^-2*arctan(a*x)+1//4*x*a^4*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3+11//8*x*a^4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3)
@test integrate(x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3, x) == :((1/2)*a^-4*c^(1/2)*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-9//20*a^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-2//15*a^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-1//20*x*a^-3*(c+c*a^2*x^2)^(1/2)+1//5*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-3//20*a^-1*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//8*x*a^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//10*a^-2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//15*a^-2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-11//20*c*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+11//20*c*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-11//20*im*c*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-11//20*im*c*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+11//20*im*c*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3, x) == :(-1//4*a^-3*(c+c*a^2*x^2)^(1/2)+1//4*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1//8*a^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//4*a^-1*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//4*x*a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//8*x*a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+(1/2)*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3//4*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+-3//4*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-1//2*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3//4*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+3//4*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3//8*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))+1//4*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+3//8*im*c*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x))))
@test integrate(x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3, x) == :(a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1*a^-2*c^(1/2)*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-1//2*x*a^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//3*a^-2*c^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+c*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-1*c*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+im*c*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+im*c*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+-1*im*c*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate((c+c*a^2*x^2)^(1/2)*arctan(a*x)^3, x) == :((1/2)*x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-3//2*a^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-3*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-3*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+3*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+3*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-1*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+-6*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3//2*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+3//2*im*c*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x))))
@test integrate(x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3, x) == :((c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-6*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+6*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-6*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+-6*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+-2*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+6*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+6*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+-6*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+-3*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))+3*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))+6*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+6*im*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3, x) == :(-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-6*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+6*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-6*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-6*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-6*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+6*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+6*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-6*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+-3*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+-2*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+3*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))+6*im*a*c*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3, x) == :(-1//2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-3//2*a*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+-6*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+-3*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+3*im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3*im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+3*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+-3//2*im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))+3//2*im*c*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x))))
@test integrate(x^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3, x) == :(-1*a^3*c^(1/2)*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1*a^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//2*a*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//3*c^-1*x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+c*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-1*c*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+-1*c*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+im*c*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+-1*im*c*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^3//2*arctan(a*x)^3, x) == :(23//120*a^-4*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-163//840*c*a^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-2//35*c*a^-4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-1//140*c*a^-1*x^3*(c+c*a^2*x^2)^(1/2)+1//35*c*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//420*c*x*a^-3*(c+c*a^2*x^2)^(1/2)+8//35*c*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-51//280*a^-4*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-23//280*c*a^-1*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//14*a*c*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//7*c*a^2*x^6*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1//35*c*a^-2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1//60*c*a^-2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+9//112*c*x*a^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+51//280*a^-4*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-51//280*im*a^-4*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-51//280*im*a^-4*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+51//280*im*a^-4*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^3//2*arctan(a*x)^3, x) == :(-1//60*a^-3*(c+c*a^2*x^2)^3//2+-1//30*c*a^-3*(c+c*a^2*x^2)^(1/2)+1//20*c*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+7//24*c*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+31//240*c*a^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-19//120*c*a^-1*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//10*a*c*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//6*c*a^2*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1//12*c*x*a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+1//16*c*x*a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-41//120*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3//8*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+-3//8*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+3//8*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+3//8*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+41//120*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3//16*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))+1//8*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+3//16*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+41//60*im*a^-3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x*(c+c*a^2*x^2)^3//2*arctan(a*x)^3, x) == :(-1//2*a^-2*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//10*a^-2*(c+c*a^2*x^2)^3//2*arctan(a*x)+-3//20*x*a^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-1//20*c*x*a^-1*(c+c*a^2*x^2)^(1/2)+1//5*a^-2*c^-1*(c+c*a^2*x^2)^5//2*arctan(a*x)^3+9//20*c*a^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-9//20*a^-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-9//40*c*x*a^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+9//20*a^-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-9//20*im*a^-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+9//20*im*a^-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+9//20*im*a^-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate((c+c*a^2*x^2)^3//2*arctan(a*x)^3, x) == :(-1//4*c*a^-1*(c+c*a^2*x^2)^(1/2)+-1//4*a^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+1//4*x*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+-9//8*c*a^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//4*c*x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+3//8*c*x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-9//4*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-9//4*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+-5//2*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+5//2*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+9//4*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+9//4*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-5*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-9//8*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+-3//4*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+9//8*im*a^-1*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x))))
@test integrate(x^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)^3, x) == :(-1*c^3//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//3*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+c*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+c*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-7*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+7*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-6*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+-6*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+-2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+6*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+6*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+-1//2*a*c*x*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-7*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+-3*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))+3*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))+7*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+7*im*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^3//2*arctan(a*x)^3, x) == :(-1*c*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-3//2*a*c*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+(1/2)*c*x*a^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-6*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+6*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-9*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-9*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+-6*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-3*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+9*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+9*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-6*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+-6*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+6*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+-9//2*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+9//2*im*a*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x))))
@test integrate(x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)^3, x) == :(c*a^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-1//2*c*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-6*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+6*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-3//2*a*c*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-9*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+-9*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+-6*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+3*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+9*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+9*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+-6*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+6*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+6*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+-9//2*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))+9//2*im*a^2*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x))))
@test integrate(x^-4*(c+c*a^2*x^2)^3//2*arctan(a*x)^3, x) == :(-1*a^3*c^3//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-1//3*x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+-1*c*a^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-1*c*a^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-7*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+7*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-1//2*a*c*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-7*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-6*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-6*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+6*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+6*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-7*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+-3*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+-2*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+3*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))+7*im*a^3*c^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^5//2*arctan(a*x)^3, x) == :(1433//15120*a^-4*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+-6157//60480*a^-4*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-2//63*a^-4*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-1//240*a^-1*c^2*x^3*(c+c*a^2*x^2)^(1/2)+-1//504*a*c^2*x^5*(c+c*a^2*x^2)^(1/2)+5//21*c^2*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+67//2520*c^2*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+85//12096*x*a^-3*c^2*(c+c*a^2*x^2)^(1/2)+-205//4032*a^-1*c^2*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-115//1344*a^-4*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-103//1008*a*c^2*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-47//30240*a^-2*c^2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-1//24*a^3*c^2*x^7*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//9*a^4*c^2*x^8*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1//63*a^-2*c^2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1//84*a^2*c^2*x^6*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+19//63*a^2*c^2*x^6*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+47//896*x*a^-3*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+115//1344*a^-4*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-115//1344*im*a^-4*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-115//1344*im*a^-4*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+115//1344*im*a^-4*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^5//2*arctan(a*x)^3, x) == :(-1//280*a^-3*(c+c*a^2*x^2)^5//2+-3//560*c*a^-3*(c+c*a^2*x^2)^3//2+13//6720*a^-3*c^2*(c+c*a^2*x^2)^(1/2)+29//560*c^2*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+59//192*c^2*x^3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1373//13440*a^-3*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-737//6720*a^-1*c^2*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-83//560*a*c^2*x^4*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-3//56*a^3*c^2*x^6*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//8*a^4*c^2*x^7*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1//56*a^2*c^2*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+5//128*x*a^-2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+17//48*a^2*c^2*x^5*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+43//1344*x*a^-2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-397//1680*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-15//64*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+-15//64*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+15//64*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+15//64*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+397//1680*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-15//128*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))+5//64*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+15//128*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+397//840*im*a^-3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2))
@test integrate(x*(c+c*a^2*x^2)^5//2*arctan(a*x)^3, x) == :(-37//120*a^-2*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//35*a^-2*(c+c*a^2*x^2)^5//2*arctan(a*x)+-17//420*x*a^-1*c^2*(c+c*a^2*x^2)^(1/2)+-1//14*x*a^-1*(c+c*a^2*x^2)^5//2*arctan(a*x)^2+-1//140*c*x*a^-1*(c+c*a^2*x^2)^3//2+1//7*a^-2*c^-1*(c+c*a^2*x^2)^7//2*arctan(a*x)^3+5//84*c*a^-2*(c+c*a^2*x^2)^3//2*arctan(a*x)+15//56*a^-2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-15//56*a^-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-15//112*x*a^-1*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-5//56*c*x*a^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+15//56*a^-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-15//56*im*a^-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+15//56*im*a^-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+15//56*im*a^-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate((c+c*a^2*x^2)^5//2*arctan(a*x)^3, x) == :(-17//60*a^-1*c^2*(c+c*a^2*x^2)^(1/2)+-1//10*a^-1*(c+c*a^2*x^2)^5//2*arctan(a*x)^2+-1//60*c*a^-1*(c+c*a^2*x^2)^3//2+1//6*x*(c+c*a^2*x^2)^5//2*arctan(a*x)^3+-15//16*a^-1*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-5//24*c*a^-1*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+1//20*c*x*(c+c*a^2*x^2)^3//2*arctan(a*x)+5//16*x*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+5//24*c*x*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+17//60*x*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-259//120*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-15//8*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-15//8*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+15//8*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+15//8*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+259//120*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-259//60*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-15//16*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+-5//8*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+15//16*im*a^-1*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x))))
@test integrate(x^-1*(c+c*a^2*x^2)^5//2*arctan(a*x)^3, x) == :(-3//2*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+1//5*(c+c*a^2*x^2)^5//2*arctan(a*x)^3+c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1//3*c*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+1//10*c*(c+c*a^2*x^2)^3//2*arctan(a*x)+29//20*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-149//20*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-1//20*a*x*c^2*(c+c*a^2*x^2)^(1/2)+149//20*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-6*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+-6*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+-2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+6*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+6*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+-29//40*a*x*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-3//20*a*c*x*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-3*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))+3*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))+-149//20*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+149//20*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+149//20*im*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-2*(c+c*a^2*x^2)^5//2*arctan(a*x)^3, x) == :(-1//4*a*c^2*(c+c*a^2*x^2)^(1/2)+-1*c^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-21//8*a*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//4*a*c*(c+c*a^2*x^2)^3//2*arctan(a*x)^2+-6*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+6*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+1//4*c*x*a^2*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+1//4*x*a^2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+7//8*x*a^2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-6*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-45//4*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-45//4*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+-11//2*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+11//2*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+45//4*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+45//4*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-11*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-6*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+6*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+-45//8*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+-15//4*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+45//8*im*a*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x))))
@test integrate(x^-3*(c+c*a^2*x^2)^5//2*arctan(a*x)^3, x) == :(-1*a^2*c^5//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+a^2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+2*a^2*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-1//2*c^2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+1//3*c*a^2*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+-13*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+13*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-3//2*a*c^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//2*x*a^3*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-15*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+-15*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+-6*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-5*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+-3*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+15*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+15*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+-13*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+13*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+13*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+-15//2*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))+15//2*im*a^2*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x))))
@test integrate(x^-4*(c+c*a^2*x^2)^5//2*arctan(a*x)^3, x) == :(-1*a^3*c^5//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-3//2*a^3*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-1//3*c*x^-3*(c+c*a^2*x^2)^3//2*arctan(a*x)^3+(1/2)*x*a^4*c^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-1*a^2*c^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-13*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+-2*a^2*c^2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+13*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-1//2*a*c^2*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-15*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-15*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+-13*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-3*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+15*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+15*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-13*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+-6*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-5*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+13*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+-15//2*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+15//2*im*a^3*c^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x))))
@test integrate(x^3*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3, x) == :(-1*a^-4*c^-1//2*arctanh(a*x*c^(1/2)*(c+c*a^2*x^2)^-1//2)+a^-4*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+-5*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+5*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-2//3*a^-4*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-1//2*x*a^-3*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+1//3*a^-2*c^-1*x^2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-5*im*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+-5*im*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x)+5*im*a^-4*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3, x) == :(-3//2*a^-3*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+(1/2)*x*a^-2*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-3*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+-3*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+3*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+3*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+-6*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctan((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3//2*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))+3//2*im*a^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x))))
@test integrate(x*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3, x) == :(a^-2*c^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-6*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+6*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-6*im*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+6*im*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+6*im*a^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate((c+c*a^2*x^2)^-1//2*arctan(a*x)^3, x) == :(-6*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-6*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+6*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+6*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-3*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+-2*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+3*im*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x))))
@test integrate(x^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3, x) == :(-6*im*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+-6*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+6*im*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+6*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+-3*im*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))+3*im*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x))))
@test integrate(x^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3, x) == :(-1*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-6*a*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+6*a*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-6*a*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-6*im*a*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+6*im*a*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^-3*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3, x) == :(-1//2*c^-1*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+-6*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)*arctanh((1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+-3*im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+-3*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+3*im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*(1+im*a*x)^(1/2)*(1+-1*im*a*x)^-1//2)+3*im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+3*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+-3//2*a*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+-3//2*im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))+3//2*im*a^2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x))))
@test integrate(x^-4*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3, x) == :(-1*a^3*c^-1//2*arctanh(c^-1//2*(c+c*a^2*x^2)^(1/2))+-5*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+5*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+-1//3*c^-1*x^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-1*a^2*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)+5*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-1//2*a*c^-1*x^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^2+2//3*a^2*c^-1*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-5*im*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x)+5*im*a^3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3, x) == :(a^-4*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+a^-4*c^-2*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-6*a^-4*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+6*x*a^-3*c^-1*(c+c*a^2*x^2)^-1//2+-6*a^-4*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-3*x*a^-3*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+6*a^-4*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-6*im*a^-4*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+6*im*a^-4*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+6*im*a^-4*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3, x) == :(6*a^-3*c^-1*(c+c*a^2*x^2)^-1//2+-3*a^-3*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1*x*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+6*x*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-6*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-6*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+6*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+6*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-3*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+-2*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+3*im*a^-3*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x))))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3, x) == :(-1*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+-6*x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2+6*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+3*x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2)
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^3, x) == :(-6*a^-1*c^-1*(c+c*a^2*x^2)^-1//2+x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+-6*x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+3*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2)
@test integrate(x^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3, x) == :(c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+-6*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+6*a*x*c^-1*(c+c*a^2*x^2)^-1//2+-6*im*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+-6*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+-3*a*x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+6*im*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+6*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+-3*im*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))+3*im*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x))))
@test integrate(x^-2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3, x) == :(6*a*c^-1*(c+c*a^2*x^2)^-1//2+-1*c^-2*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-3*a*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1*x*a^2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+-6*a*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+6*a*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+6*x*a^2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-6*a*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-6*im*a*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+6*im*a*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^5*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3, x) == :(a^-6*c^-3*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-94//9*a^-6*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+2//27*a^-3*c^-1*x^3*(c+c*a^2*x^2)^-3//2+5//3*a^-6*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+94//9*x*a^-5*c^-2*(c+c*a^2*x^2)^-1//2+-6*a^-6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))+-5*x*a^-5*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+6*a^-6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))+-2//9*a^-4*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)+-1//3*a^-3*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+1//3*a^-4*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3+-6*im*a^-6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+6*im*a^-6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctan(exp(im*arctan(a*x)))+6*im*a^-6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate(x^4*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3, x) == :(-2//27*a^-5*c^-1*(c+c*a^2*x^2)^-3//2+68//9*a^-5*c^-2*(c+c*a^2*x^2)^-1//2+-11//3*a^-5*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1*x*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+-1//3*a^-3*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+-1//3*a^-2*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3+2//9*a^-2*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)+22//3*x*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-6*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*im*exp(im*arctan(a*x)))+-6*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*im*exp(im*arctan(a*x)))*arctan(a*x)+6*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,im*exp(im*arctan(a*x)))+6*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,im*exp(im*arctan(a*x)))*arctan(a*x)+-3*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arctan(a*x)))+-2*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctan(exp(im*arctan(a*x)))+3*im*a^-5*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arctan(a*x))))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3, x) == :(-40//9*x*a^-3*c^-2*(c+c*a^2*x^2)^-1//2+-2//3*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+-2//27*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2+40//9*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+2*x*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1//3*a^-2*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3+1//3*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+2//9*a^-2*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3, x) == :(-14//9*a^-3*c^-2*(c+c*a^2*x^2)^-1//2+2//27*a^-3*c^-1*(c+c*a^2*x^2)^-3//2+-2//9*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)+1//3*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3+2//3*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-4//3*x*a^-2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+1//3*a^-1*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2)
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3, x) == :(-40//27*x*a^-1*c^-2*(c+c*a^2*x^2)^-1//2+-2//27*x*a^-1*c^-1*(c+c*a^2*x^2)^-3//2+-1//3*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3+2//9*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+4//3*a^-2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+1//3*x*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+2//3*x*a^-1*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2)
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^3, x) == :(-40//9*a^-1*c^-2*(c+c*a^2*x^2)^-1//2+-2//27*a^-1*c^-1*(c+c*a^2*x^2)^-3//2+2*a^-1*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-40//9*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-2//9*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+1//3*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3+1//3*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+2//3*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3)
@test integrate(x^-1*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3, x) == :(c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+-22//3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-2//9*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+1//3*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3+2//27*a*x*c^-1*(c+c*a^2*x^2)^-3//2+202//27*a*x*c^-2*(c+c*a^2*x^2)^-1//2+-6*im*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,-1*exp(im*arctan(a*x)))+-6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))*arctan(a*x)+-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3*arctanh(exp(im*arctan(a*x)))+6*im*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(4,exp(im*arctan(a*x)))+6*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))*arctan(a*x)+-11//3*a*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1//3*a*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+-3*im*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))+3*im*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x))))
@test integrate(x^-2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3, x) == :(2//27*a*c^-1*(c+c*a^2*x^2)^-3//2+94//9*a*c^-2*(c+c*a^2*x^2)^-1//2+-1*c^-3*x^-1*(c+c*a^2*x^2)^(1/2)*arctan(a*x)^3+-5*a*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2+-1//3*a*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^2+-6*a*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arctan(a*x)))+6*a*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arctan(a*x)))+-5//3*x*a^2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3+-1//3*x*a^2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3+2//9*x*a^2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)+94//9*x*a^2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)+-6*a*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^2*arctanh(exp(im*arctan(a*x)))+-6*im*a*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arctan(a*x)))*arctan(a*x)+6*im*a*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arctan(a*x)))*arctan(a*x))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^-1, x) == :(a^-1*c^-1*log(arctan(a*x)))
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^-1, x) == :((1/2)*a^-3*c^-2*log(arctan(a*x))+-1//2*a^-3*c^-2*cosintegral(2*arctan(a*x)))
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^-1, x) == :((1/2)*a^-2*c^-2*sinintegral(2*arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^-1, x) == :((1/2)*a^-1*c^-2*cosintegral(2*arctan(a*x))+(1/2)*a^-1*c^-2*log(arctan(a*x)))
@test integrate(x^4*(c+c*a^2*x^2)^-3*arctan(a*x)^-1, x) == :(-1//2*a^-5*c^-3*cosintegral(2*arctan(a*x))+1//8*a^-5*c^-3*cosintegral(4*arctan(a*x))+3//8*a^-5*c^-3*log(arctan(a*x)))
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^-1, x) == :(-1//8*a^-4*c^-3*sinintegral(4*arctan(a*x))+1//4*a^-4*c^-3*sinintegral(2*arctan(a*x)))
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^-1, x) == :(-1//8*a^-3*c^-3*cosintegral(4*arctan(a*x))+1//8*a^-3*c^-3*log(arctan(a*x)))
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^-1, x) == :(1//4*a^-2*c^-3*sinintegral(2*arctan(a*x))+1//8*a^-2*c^-3*sinintegral(4*arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^-1, x) == :((1/2)*a^-1*c^-3*cosintegral(2*arctan(a*x))+1//8*a^-1*c^-3*cosintegral(4*arctan(a*x))+3//8*a^-1*c^-3*log(arctan(a*x)))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1, x) == :(a^-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^-1, x) == :(a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(arctan(a*x)))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-1, x) == :(-1//4*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(3*arctan(a*x))+3//4*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(arctan(a*x)))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-1, x) == :(-1//4*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(3*arctan(a*x))+1//4*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(arctan(a*x)))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-1, x) == :(1//4*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(3*arctan(a*x))+1//4*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^-1, x) == :(1//4*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(3*arctan(a*x))+3//4*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^-2, x) == :(-1*a^-1*c^-1*arctan(a*x)^-1)
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^-2, x) == :(a^-3*c^-2*sinintegral(2*arctan(a*x))+-1*a^-1*c^-2*x^2*(1+a^2*x^2)^-1*arctan(a*x)^-1)
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^-2, x) == :(a^-2*c^-2*cosintegral(2*arctan(a*x))+-1*x*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1)
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^-2, x) == :(-1*a^-1*c^-2*sinintegral(2*arctan(a*x))+-1*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1)
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^-2, x) == :((1/2)*a^-4*c^-3*cosintegral(2*arctan(a*x))+-1//2*a^-4*c^-3*cosintegral(4*arctan(a*x))+x*a^-3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1+-1*x*a^-3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^-1)
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^-2, x) == :((1/2)*a^-3*c^-3*sinintegral(4*arctan(a*x))+a^-3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1+-1*a^-3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^-1)
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^-2, x) == :((1/2)*a^-2*c^-3*cosintegral(2*arctan(a*x))+(1/2)*a^-2*c^-3*cosintegral(4*arctan(a*x))+-1*x*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1)
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^-2, x) == :(-1*a^-1*c^-3*sinintegral(2*arctan(a*x))+-1//2*a^-1*c^-3*sinintegral(4*arctan(a*x))+-1*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1)
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-2, x) == :(a^-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(arctan(a*x))+-1*x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1)
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^-2, x) == :(-1*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1+-1*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(arctan(a*x)))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-2, x) == :(-1*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1+-3//4*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(3*arctan(a*x))+3//4*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(arctan(a*x)))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-2, x) == :(a^-3*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1+-1*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1+-1//4*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(arctan(a*x))+3//4*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(3*arctan(a*x)))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-2, x) == :(-1*x*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1+1//4*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(arctan(a*x))+3//4*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(3*arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^-2, x) == :(-1*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1+-3//4*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(3*arctan(a*x))+-3//4*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^-3, x) == :(-1//2*a^-1*c^-1*arctan(a*x)^-2)
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^-3, x) == :(a^-3*c^-2*cosintegral(2*arctan(a*x))+-1*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1+-1//2*a^-1*c^-2*x^2*(1+a^2*x^2)^-1*arctan(a*x)^-2)
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^-3, x) == :(-1*a^-2*c^-2*sinintegral(2*arctan(a*x))+-1//2*x*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-2+-1//2*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1*(1+-1*a^2*x^2))
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^-3, x) == :(-1*a^-1*c^-2*cosintegral(2*arctan(a*x))+x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1+-1//2*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-2)
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^-3, x) == :(a^-4*c^-3*sinintegral(4*arctan(a*x))+-1//2*a^-4*c^-3*sinintegral(2*arctan(a*x))+2*a^-4*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1+-3//2*a^-4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^-1+(1/2)*x*a^-3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-2+-1//2*x*a^-3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^-2+-1//2*a^-4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^-1*(1+-1*a^2*x^2))
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^-3, x) == :(a^-3*c^-3*cosintegral(4*arctan(a*x))+(1/2)*a^-3*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-2+-1//2*a^-3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^-2+x*a^-2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^-1+-2*x*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1)
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^-3, x) == :(-1*a^-2*c^-3*sinintegral(4*arctan(a*x))+-1//2*a^-2*c^-3*sinintegral(2*arctan(a*x))+-2*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1+3//2*a^-2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^-1+-1//2*x*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-2)
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^-3, x) == :(-1*a^-1*c^-3*cosintegral(2*arctan(a*x))+-1*a^-1*c^-3*cosintegral(4*arctan(a*x))+2*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1+-1//2*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-2)
@test integrate(x^3*(1+a^2*x^2)^-1*arctan(a*x)^-3+-3//2*a^-1*x^2*arctan(a*x)^-2, x) == :(-1//2*a^-1*x^3*arctan(a*x)^-2)
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-3, x) == :(-1//2*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1+-1//2*x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-2+-1//2*a^-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^-3, x) == :((1/2)*x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1+-1//2*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-2+-1//2*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(arctan(a*x)))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-3, x) == :(-3//2*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1+3//2*a^-4*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1+-3//8*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(arctan(a*x))+-1//2*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-2+9//8*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(3*arctan(a*x)))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-3, x) == :((1/2)*a^-3*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-2+-1//2*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-2+(1/2)*x*a^-2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1+-3//2*x*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1+-1//8*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(arctan(a*x))+9//8*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(3*arctan(a*x)))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-3, x) == :(a^-2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1+-3//2*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1+-9//8*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(3*arctan(a*x))+-1//2*x*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-2+-1//8*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*sinintegral(arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^-3, x) == :(-1//2*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-2+3//2*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1+-9//8*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(3*arctan(a*x))+-3//8*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*cosintegral(arctan(a*x)))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^(1/2), x) == :(2//3*a^-1*c^-1*arctan(a*x)^3//2)
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^(1/2), x) == :(1//3*a^-3*c^-2*arctan(a*x)^3//2+1//8*pi^(1/2)*a^-3*c^-2*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-1//2*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2))
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^(1/2), x) == :(1//4*a^-2*c^-2*arctan(a*x)^(1/2)+-1//2*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+1//8*pi^(1/2)*a^-2*c^-2*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^(1/2), x) == :(1//3*a^-1*c^-2*arctan(a*x)^3//2+(1/2)*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+-1//8*pi^(1/2)*a^-1*c^-2*fresnels(2*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^4*(c+c*a^2*x^2)^-3*arctan(a*x)^(1/2), x) == :(1//4*a^-5*c^-3*arctan(a*x)^3//2+-1//4*a^-5*c^-3*arctan(a*x)^(1/2)*sin(2*arctan(a*x))+1//8*pi^(1/2)*a^-5*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+1//32*a^-5*c^-3*arctan(a*x)^(1/2)*sin(4*arctan(a*x))+-1//128*2^(1/2)*pi^(1/2)*a^-5*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^(1/2), x) == :(-3//32*a^-4*c^-3*arctan(a*x)^(1/2)+1//4*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)^(1/2)+1//16*pi^(1/2)*a^-4*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-1//128*2^(1/2)*pi^(1/2)*a^-4*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^(1/2), x) == :(1//12*a^-3*c^-3*arctan(a*x)^3//2+-1//32*a^-3*c^-3*arctan(a*x)^(1/2)*sin(4*arctan(a*x))+1//128*2^(1/2)*pi^(1/2)*a^-3*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^(1/2), x) == :(3//32*a^-2*c^-3*arctan(a*x)^(1/2)+-1//4*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^(1/2)+1//16*pi^(1/2)*a^-2*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+1//128*2^(1/2)*pi^(1/2)*a^-2*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^(1/2), x) == :(1//4*a^-1*c^-3*arctan(a*x)^3//2+-1//8*pi^(1/2)*a^-1*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+1//4*a^-1*c^-3*arctan(a*x)^(1/2)*sin(2*arctan(a*x))+1//32*a^-1*c^-3*arctan(a*x)^(1/2)*sin(4*arctan(a*x))+-1//128*2^(1/2)*pi^(1/2)*a^-1*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^(1/2), x) == :(-1*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+(1/2)*2^(1/2)*pi^(1/2)*a^-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^(1/2), x) == :(x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+-1//2*2^(1/2)*pi^(1/2)*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^(1/2), x) == :(-3//4*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+1//12*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)*cos(3*arctan(a*x))+-1//72*6^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+3//8*2^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^(1/2), x) == :(1//3*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^(1/2)+-1//8*2^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+1//72*6^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^(1/2), x) == :(-1//3*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^(1/2)+1//8*2^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+1//72*6^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^(1/2), x) == :(3//4*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+1//12*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)*sin(3*arctan(a*x))+-3//8*2^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1//72*6^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^3//2, x) == :(2//5*a^-1*c^-1*arctan(a*x)^5//2)
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^3//2, x) == :(1//5*a^-3*c^-2*arctan(a*x)^5//2+3//16*a^-3*c^-2*arctan(a*x)^(1/2)+-3//8*a^-3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+3//32*pi^(1/2)*a^-3*c^-2*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-1//2*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3//2)
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^3//2, x) == :(1//4*a^-2*c^-2*arctan(a*x)^3//2+-3//32*pi^(1/2)*a^-2*c^-2*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-1//2*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3//2+3//8*x*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2))
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^3//2, x) == :(-3//16*a^-1*c^-2*arctan(a*x)^(1/2)+1//5*a^-1*c^-2*arctan(a*x)^5//2+(1/2)*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3//2+-3//32*pi^(1/2)*a^-1*c^-2*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+3//8*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2))
@test integrate(x^4*(c+c*a^2*x^2)^-3*arctan(a*x)^3//2, x) == :(3//20*a^-5*c^-3*arctan(a*x)^5//2+27//256*a^-5*c^-3*arctan(a*x)^(1/2)+-9//32*a^-5*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+3//32*pi^(1/2)*a^-5*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-3//8*x*a^-4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3//2+-3//1024*2^(1/2)*pi^(1/2)*a^-5*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1//4*a^-2*c^-3*x^3*(1+a^2*x^2)^-2*arctan(a*x)^3//2+3//32*a^-1*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)^(1/2))
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^3//2, x) == :(-3//32*a^-4*c^-3*arctan(a*x)^3//2+-3//64*pi^(1/2)*a^-4*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-3//256*a^-4*c^-3*arctan(a*x)^(1/2)*sin(4*arctan(a*x))+1//4*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)^3//2+3//32*a^-4*c^-3*arctan(a*x)^(1/2)*sin(2*arctan(a*x))+3//1024*2^(1/2)*pi^(1/2)*a^-4*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^3//2, x) == :(1//20*a^-3*c^-3*arctan(a*x)^5//2+-3//256*a^-3*c^-3*arctan(a*x)^(1/2)*cos(4*arctan(a*x))+-1//32*a^-3*c^-3*arctan(a*x)^3//2*sin(4*arctan(a*x))+3//1024*2^(1/2)*pi^(1/2)*a^-3*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^3//2, x) == :(3//32*a^-2*c^-3*arctan(a*x)^3//2+-3//64*pi^(1/2)*a^-2*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-1//4*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3//2+3//32*a^-2*c^-3*arctan(a*x)^(1/2)*sin(2*arctan(a*x))+3//256*a^-2*c^-3*arctan(a*x)^(1/2)*sin(4*arctan(a*x))+-3//1024*2^(1/2)*pi^(1/2)*a^-2*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^3//2, x) == :(-45//256*a^-1*c^-3*arctan(a*x)^(1/2)+3//20*a^-1*c^-3*arctan(a*x)^5//2+-3//32*pi^(1/2)*a^-1*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+1//4*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3//2+3//8*x*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3//2+3//32*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^(1/2)+9//32*a^-1*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+-3//1024*2^(1/2)*pi^(1/2)*a^-1*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2, x) == :(-1*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+3//2*x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+-3//4*2^(1/2)*pi^(1/2)*a^-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2, x) == :(x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+3//2*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+-3//4*2^(1/2)*pi^(1/2)*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3//2, x) == :(-2//3*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+x*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+-1//3*a^-2*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2+1//6*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^(1/2)+-9//16*2^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+1//144*6^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3//2, x) == :(1//3*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2+3//8*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+-1//24*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)*cos(3*arctan(a*x))+-3//16*2^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+1//144*6^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^3//2, x) == :(-1//3*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2+3//8*x*a^-1*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+1//24*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)*sin(3*arctan(a*x))+-3//16*2^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1//144*6^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^3//2, x) == :(a^-1*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+1//3*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2+1//6*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^(1/2)+2//3*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+-9//16*2^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1//144*6^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^5//2, x) == :(2//7*a^-1*c^-1*arctan(a*x)^7//2)
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^5//2, x) == :(1//7*a^-3*c^-2*arctan(a*x)^7//2+5//16*a^-3*c^-2*arctan(a*x)^3//2+-15//128*pi^(1/2)*a^-3*c^-2*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-5//8*a^-3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3//2+-1//2*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^5//2+15//32*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2))
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^5//2, x) == :(-15//64*a^-2*c^-2*arctan(a*x)^(1/2)+1//4*a^-2*c^-2*arctan(a*x)^5//2+-15//128*pi^(1/2)*a^-2*c^-2*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-1//2*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^5//2+15//32*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+5//8*x*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3//2)
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^5//2, x) == :(-5//16*a^-1*c^-2*arctan(a*x)^3//2+1//7*a^-1*c^-2*arctan(a*x)^7//2+(1/2)*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^5//2+-15//32*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+5//8*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^3//2+15//128*pi^(1/2)*a^-1*c^-2*fresnels(2*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^4*(c+c*a^2*x^2)^-3*arctan(a*x)^5//2, x) == :(3//28*a^-5*c^-3*arctan(a*x)^7//2+45//256*a^-5*c^-3*arctan(a*x)^3//2+-15//32*a^-5*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3//2+-15//128*pi^(1/2)*a^-5*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-15//2048*a^-5*c^-3*arctan(a*x)^(1/2)*sin(4*arctan(a*x))+15//256*a^-5*c^-3*arctan(a*x)^(1/2)*sin(2*arctan(a*x))+-3//8*x*a^-4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^5//2+-1//4*a^-2*c^-3*x^3*(1+a^2*x^2)^-2*arctan(a*x)^5//2+5//32*a^-1*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)^3//2+15//8192*2^(1/2)*pi^(1/2)*a^-5*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+45//128*x*a^-4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^(1/2))
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^5//2, x) == :(-135//2048*a^-4*c^-3*arctan(a*x)^(1/2)+-3//32*a^-4*c^-3*arctan(a*x)^5//2+-15//256*pi^(1/2)*a^-4*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-15//256*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)^(1/2)+1//4*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)^5//2+45//256*a^-4*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+5//32*a^-1*c^-3*x^3*(1+a^2*x^2)^-2*arctan(a*x)^3//2+15//64*x*a^-3*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3//2+15//8192*2^(1/2)*pi^(1/2)*a^-4*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^5//2, x) == :(1//28*a^-3*c^-3*arctan(a*x)^7//2+-5//256*a^-3*c^-3*arctan(a*x)^3//2*cos(4*arctan(a*x))+-1//32*a^-3*c^-3*arctan(a*x)^5//2*sin(4*arctan(a*x))+15//2048*a^-3*c^-3*arctan(a*x)^(1/2)*sin(4*arctan(a*x))+-15//8192*2^(1/2)*pi^(1/2)*a^-3*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^5//2, x) == :(-225//2048*a^-2*c^-3*arctan(a*x)^(1/2)+3//32*a^-2*c^-3*arctan(a*x)^5//2+-15//256*pi^(1/2)*a^-2*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-1//4*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^5//2+15//256*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^(1/2)+45//256*a^-2*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+-15//8192*2^(1/2)*pi^(1/2)*a^-2*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+5//32*x*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3//2+15//64*x*a^-1*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3//2)
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^5//2, x) == :(-75//256*a^-1*c^-3*arctan(a*x)^3//2+3//28*a^-1*c^-3*arctan(a*x)^7//2+-45//128*x*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+-15//256*a^-1*c^-3*arctan(a*x)^(1/2)*sin(2*arctan(a*x))+-15//2048*a^-1*c^-3*arctan(a*x)^(1/2)*sin(4*arctan(a*x))+1//4*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^5//2+3//8*x*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^5//2+5//32*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^3//2+15//32*a^-1*c^-3*(1+a^2*x^2)^-1*arctan(a*x)^3//2+15//128*pi^(1/2)*a^-1*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+15//8192*2^(1/2)*pi^(1/2)*a^-1*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^5//2, x) == :(-1*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^5//2+15//4*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+5//2*x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+-15//8*2^(1/2)*pi^(1/2)*a^-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^5//2, x) == :(x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^5//2+-15//4*x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+5//2*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+15//8*2^(1/2)*pi^(1/2)*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^5//2, x) == :(-2//3*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^5//2+45//16*a^-4*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+-1//3*a^-2*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^5//2+5//3*x*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+5//18*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2+-5//144*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)*cos(3*arctan(a*x))+-45//32*2^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+5//864*6^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^5//2, x) == :(-5//36*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^(1/2)+1//3*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^5//2+5//9*a^-3*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+-5//6*x*a^-2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+5//18*a^-1*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2+-5//864*6^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+15//32*2^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^5//2, x) == :(-1//3*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^5//2+5//6*a^-2*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+5//36*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^(1/2)+5//9*x*a^-1*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+5//18*x*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2+-15//32*2^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-5//864*6^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^5//2, x) == :(-45//16*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)+1//3*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^5//2+2//3*x*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^5//2+5//3*a^-1*c^-2*(c+c*a^2*x^2)^-1//2*arctan(a*x)^3//2+5//18*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^3//2+-5//144*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arctan(a*x)^(1/2)*sin(3*arctan(a*x))+5//864*6^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+45//32*2^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^-1//2, x) == :(2*a^-1*c^-1*arctan(a*x)^(1/2))
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^-1//2, x) == :(a^-3*c^-2*arctan(a*x)^(1/2)+-1//2*pi^(1/2)*a^-3*c^-2*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^-1//2, x) == :((1/2)*pi^(1/2)*a^-2*c^-2*fresnels(2*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^-1//2, x) == :(a^-1*c^-2*arctan(a*x)^(1/2)+(1/2)*pi^(1/2)*a^-1*c^-2*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^4*(c+c*a^2*x^2)^-3*arctan(a*x)^-1//2, x) == :(3//4*a^-5*c^-3*arctan(a*x)^(1/2)+-1//2*pi^(1/2)*a^-5*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+1//16*2^(1/2)*pi^(1/2)*a^-5*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^-1//2, x) == :(1//4*pi^(1/2)*a^-4*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-1//16*2^(1/2)*pi^(1/2)*a^-4*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^-1//2, x) == :(1//4*a^-3*c^-3*arctan(a*x)^(1/2)+-1//16*2^(1/2)*pi^(1/2)*a^-3*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^-1//2, x) == :(1//4*pi^(1/2)*a^-2*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+1//16*2^(1/2)*pi^(1/2)*a^-2*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^-1//2, x) == :(3//4*a^-1*c^-3*arctan(a*x)^(1/2)+(1/2)*pi^(1/2)*a^-1*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+1//16*2^(1/2)*pi^(1/2)*a^-1*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2, x) == :(2^(1/2)*pi^(1/2)*a^-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2, x) == :(2^(1/2)*pi^(1/2)*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-1//2, x) == :(-1//12*6^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+3//4*2^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-1//2, x) == :(-1//12*6^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+1//4*2^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-1//2, x) == :(1//4*2^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+1//12*6^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^-1//2, x) == :(1//12*6^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+3//4*2^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^-3//2, x) == :(-2*a^-1*c^-1*arctan(a*x)^-1//2)
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^-3//2, x) == :(2*pi^(1/2)*a^-3*c^-2*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-2*a^-1*c^-2*x^2*(1+a^2*x^2)^-1*arctan(a*x)^-1//2)
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^-3//2, x) == :(4*a^-2*c^-2*arctan(a*x)^(1/2)+-8*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+2*pi^(1/2)*a^-2*c^-2*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)*(4+-4*a^2*x^2)+-2*x*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1//2)
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^-3//2, x) == :(-2*pi^(1/2)*a^-1*c^-2*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-2*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1//2)
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^-3//2, x) == :(pi^(1/2)*a^-4*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-2*a^-1*c^-3*x^3*(1+a^2*x^2)^-2*arctan(a*x)^-1//2+-1//2*2^(1/2)*pi^(1/2)*a^-4*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^-3//2, x) == :((1/2)*2^(1/2)*pi^(1/2)*a^-3*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-2*a^-1*c^-3*x^2*(1+a^2*x^2)^-2*arctan(a*x)^-1//2)
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^-3//2, x) == :(pi^(1/2)*a^-2*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+(1/2)*2^(1/2)*pi^(1/2)*a^-2*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-2*x*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1//2)
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^-3//2, x) == :(-2*pi^(1/2)*a^-1*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-2*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1//2+-1//2*2^(1/2)*pi^(1/2)*a^-1*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-3//2, x) == :(-2*x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1//2+2*2^(1/2)*pi^(1/2)*a^-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^-3//2, x) == :(-2*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1//2+-2*2^(1/2)*pi^(1/2)*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-3//2, x) == :(-2*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+-1//2*6^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+3//2*2^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-3//2, x) == :(-2*a^-1*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+(1/2)*6^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1//2*2^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-3//2, x) == :(-2*x*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+(1/2)*2^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+(1/2)*6^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^-3//2, x) == :(-2*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+-3//2*2^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1//2*6^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^-5//2, x) == :(-2//3*a^-1*c^-1*arctan(a*x)^-3//2)
@test integrate(x^2*(c+c*a^2*x^2)^-2*arctan(a*x)^-5//2, x) == :(16//3*a^-3*c^-2*arctan(a*x)^(1/2)+-32//3*a^-3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+8//3*pi^(1/2)*a^-3*c^-2*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-8//3*x*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1//2+-2//3*a^-1*c^-2*x^2*(1+a^2*x^2)^-1*arctan(a*x)^-3//2+1//3*a^-3*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)*(16+-16*a^2*x^2))
@test integrate(x*(c+c*a^2*x^2)^-2*arctan(a*x)^-5//2, x) == :(-8//3*pi^(1/2)*a^-2*c^-2*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-2//3*x*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-3//2+-1//3*a^-2*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1//2*(4+-4*a^2*x^2))
@test integrate((c+c*a^2*x^2)^-2*arctan(a*x)^-5//2, x) == :(-16//3*a^-1*c^-2*arctan(a*x)^(1/2)+-8//3*pi^(1/2)*a^-1*c^-2*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-2//3*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-3//2+8//3*x*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^-1//2+32//3*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)+-1//3*a^-1*c^-2*(1+a^2*x^2)^-1*arctan(a*x)^(1/2)*(16+-16*a^2*x^2))
@test integrate(x^3*(c+c*a^2*x^2)^-3*arctan(a*x)^-5//2, x) == :(-4//3*pi^(1/2)*a^-4*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+4//3*c^-3*x^4*(1+a^2*x^2)^-2*arctan(a*x)^-1//2+-4*a^-2*c^-3*x^2*(1+a^2*x^2)^-2*arctan(a*x)^-1//2+-2//3*a^-1*c^-3*x^3*(1+a^2*x^2)^-2*arctan(a*x)^-3//2+4//3*2^(1/2)*pi^(1/2)*a^-4*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-3*arctan(a*x)^-5//2, x) == :(8//3*c^-3*x^3*(1+a^2*x^2)^-2*arctan(a*x)^-1//2+-8//3*x*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1//2+-2//3*a^-1*c^-3*x^2*(1+a^2*x^2)^-2*arctan(a*x)^-3//2+4//3*2^(1/2)*pi^(1/2)*a^-3*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3*arctan(a*x)^-5//2, x) == :(4*c^-3*x^2*(1+a^2*x^2)^-2*arctan(a*x)^-1//2+-4//3*pi^(1/2)*a^-2*c^-3*fresnels(2*pi^-1//2*arctan(a*x)^(1/2))+-4//3*a^-2*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1//2+-4//3*2^(1/2)*pi^(1/2)*a^-2*c^-3*fresnels(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-2//3*x*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-3//2)
@test integrate((c+c*a^2*x^2)^-3*arctan(a*x)^-5//2, x) == :(-8//3*pi^(1/2)*a^-1*c^-3*fresnelc(2*pi^-1//2*arctan(a*x)^(1/2))+-2//3*a^-1*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-3//2+16//3*x*c^-3*(1+a^2*x^2)^-2*arctan(a*x)^-1//2+-4//3*2^(1/2)*pi^(1/2)*a^-1*c^-3*fresnelc(2*2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-5//2, x) == :(-4//3*a^-2*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1//2+-2//3*x*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-3//2+-4//3*2^(1/2)*pi^(1/2)*a^-2*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-3//2*arctan(a*x)^-5//2, x) == :(-2//3*a^-1*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-3//2+4//3*x*c^-1*(c+c*a^2*x^2)^-1//2*arctan(a*x)^-1//2+-4//3*2^(1/2)*pi^(1/2)*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^3*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-5//2, x) == :(-4*a^-2*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+-2//3*a^-1*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-3//2+6^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1*2^(1/2)*pi^(1/2)*a^-4*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x^2*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-5//2, x) == :(4//3*c^-1*x^3*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+-8//3*x*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+-2//3*a^-1*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-3//2+6^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1//3*2^(1/2)*pi^(1/2)*a^-3*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate(x*(c+c*a^2*x^2)^-5//2*arctan(a*x)^-5//2, x) == :(-4//3*a^-2*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+8//3*c^-1*x^2*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+-2//3*x*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-3//2+-1*6^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1//3*2^(1/2)*pi^(1/2)*a^-2*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnels(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-5//2*arctan(a*x)^-5//2, x) == :(4*x*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-1//2+-2//3*a^-1*c^-1*(c+c*a^2*x^2)^-3//2*arctan(a*x)^-3//2+-1*2^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(2^(1/2)*pi^-1//2*arctan(a*x)^(1/2))+-1*6^(1/2)*pi^(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*fresnelc(6^(1/2)*pi^-1//2*arctan(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1*arctan(a*x)^n, x) == :(a^-1*c^-1*(1+n)^-1*arctan(a*x)^(1+n))
@test integrate(x^3*(a+b*arctan(c*x))*(d+e*x^2), x) == :(1//4*d*x^4*(a+b*arctan(c*x))+1//6*e*x^6*(a+b*arctan(c*x))+-1//12*b*c^-6*(-2*e+3*d*c^2)*arctan(c*x)+-1//30*b*e*c^-1*x^5+-1//36*b*c^-3*x^3*(-2*e+3*d*c^2)+1//12*b*x*c^-5*(-2*e+3*d*c^2))
@test integrate(x^2*(a+b*arctan(c*x))*(d+e*x^2), x) == :(1//3*d*x^3*(a+b*arctan(c*x))+1//5*e*x^5*(a+b*arctan(c*x))+-1//20*b*e*c^-1*x^4+-1//30*b*c^-3*x^2*(-3*e+5*d*c^2)+1//30*b*c^-5*(-3*e+5*d*c^2)*log(1+c^2*x^2))
@test integrate(x*(a+b*arctan(c*x))*(d+e*x^2), x) == :(1//4*e^-1*(d+e*x^2)^2*(a+b*arctan(c*x))+-1//4*b*x*c^-3*(-1*e+2*d*c^2)+-1//12*b*e*c^-1*x^3+-1//4*b*c^-4*e^-1*(-1*e+d*c^2)^2*arctan(c*x))
@test integrate((a+b*arctan(c*x))*(d+e*x^2), x) == :(d*x*(a+b*arctan(c*x))+1//3*e*x^3*(a+b*arctan(c*x))+-1//6*b*e*c^-1*x^2+-1//6*b*c^-3*(-1*e+3*d*c^2)*log(1+c^2*x^2))
@test integrate(x^-1*(a+b*arctan(c*x))*(d+e*x^2), x) == :(a*d*log(x)+(1/2)*e*x^2*(a+b*arctan(c*x))+(1/2)*im*b*d*Polylogarithms.polylog(2,-1*im*c*x)+(1/2)*b*e*c^-2*arctan(c*x)+-1//2*im*b*d*Polylogarithms.polylog(2,im*c*x)+-1//2*b*e*x*c^-1)
@test integrate(x^-2*(a+b*arctan(c*x))*(d+e*x^2), x) == :(e*x*(a+b*arctan(c*x))+-1*d*x^-1*(a+b*arctan(c*x))+b*c*d*log(x)+-1//2*b*c^-1*(e+d*c^2)*log(1+c^2*x^2))
@test integrate(x^-3*(a+b*arctan(c*x))*(d+e*x^2), x) == :(a*e*log(x)+-1//2*d*x^-2*(a+b*arctan(c*x))+(1/2)*im*b*e*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*e*Polylogarithms.polylog(2,im*c*x)+-1//2*b*c*d*x^-1+-1//2*b*d*c^2*arctan(c*x))
@test integrate(x^-4*(a+b*arctan(c*x))*(d+e*x^2), x) == :(-1*e*x^-1*(a+b*arctan(c*x))+-1//3*d*x^-3*(a+b*arctan(c*x))+-1//3*b*c*(-3*e+d*c^2)*log(x)+-1//6*b*c*d*x^-2+1//6*b*c*(-3*e+d*c^2)*log(1+c^2*x^2))
@test integrate(x^-5*(a+b*arctan(c*x))*(d+e*x^2), x) == :(-1//2*e*x^-2*(a+b*arctan(c*x))+-1//4*d*x^-4*(a+b*arctan(c*x))+-1//12*b*c*d*x^-3+1//4*b*c*x^-1*(-2*e+d*c^2)+1//4*b*c^2*(-2*e+d*c^2)*arctan(c*x))
@test integrate(x^-6*(a+b*arctan(c*x))*(d+e*x^2), x) == :(-1//3*e*x^-3*(a+b*arctan(c*x))+-1//5*d*x^-5*(a+b*arctan(c*x))+-1//20*b*c*d*x^-4+-1//30*b*c^3*(-5*e+3*d*c^2)*log(1+c^2*x^2)+1//15*b*c^3*(-5*e+3*d*c^2)*log(x)+1//30*b*c*x^-2*(-5*e+3*d*c^2))
@test integrate(x^-7*(a+b*arctan(c*x))*(d+e*x^2), x) == :(-1//4*e*x^-4*(a+b*arctan(c*x))+-1//6*d*x^-6*(a+b*arctan(c*x))+-1//12*b*c^3*x^-1*(-3*e+2*d*c^2)+-1//12*b*c^4*(-3*e+2*d*c^2)*arctan(c*x)+-1//30*b*c*d*x^-5+1//36*b*c*x^-3*(-3*e+2*d*c^2))
@test integrate(x^3*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(1//4*d^2*x^4*(a+b*arctan(c*x))+1//8*e^2*x^8*(a+b*arctan(c*x))+-1//24*b*c^-8*(3*e^2+6*c^4*d^2+-8*d*e*c^2)*arctan(c*x)+-1//56*b*c^-1*e^2*x^7+-1//72*b*c^-5*x^3*(3*e^2+6*c^4*d^2+-8*d*e*c^2)+1//3*d*e*x^6*(a+b*arctan(c*x))+1//24*b*x*c^-7*(3*e^2+6*c^4*d^2+-8*d*e*c^2)+-1//120*b*e*c^-3*x^5*(-3*e+8*d*c^2))
@test integrate(x^2*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(1//3*d^2*x^3*(a+b*arctan(c*x))+1//7*e^2*x^7*(a+b*arctan(c*x))+-1//42*b*c^-1*e^2*x^6+-1//210*b*c^-5*x^2*(15*e^2+35*c^4*d^2+-42*d*e*c^2)+1//210*b*c^-7*(15*e^2+35*c^4*d^2+-42*d*e*c^2)*log(1+c^2*x^2)+2//5*d*e*x^5*(a+b*arctan(c*x))+-1//140*b*e*c^-3*x^4*(-5*e+14*d*c^2))
@test integrate(x*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(1//6*e^-1*(d+e*x^2)^3*(a+b*arctan(c*x))+-1//6*b*x*c^-5*(e^2+3*c^4*d^2+-3*d*e*c^2)+-1//30*b*c^-1*e^2*x^5+-1//6*b*c^-6*e^-1*(-1*e+d*c^2)^3*arctan(c*x)+-1//18*b*e*c^-3*x^3*(-1*e+3*d*c^2))
@test integrate((d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(x*d^2*(a+b*arctan(c*x))+1//5*e^2*x^5*(a+b*arctan(c*x))+-1//20*b*c^-1*e^2*x^4+-1//30*b*c^-5*(3*e^2+15*c^4*d^2+-10*d*e*c^2)*log(1+c^2*x^2)+2//3*d*e*x^3*(a+b*arctan(c*x))+-1//30*b*e*c^-3*x^2*(-3*e+10*d*c^2))
@test integrate(x^-1*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(a*d^2*log(x)+1//4*e^2*x^4*(a+b*arctan(c*x))+d*e*x^2*(a+b*arctan(c*x))+(1/2)*im*b*d^2*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*d^2*Polylogarithms.polylog(2,im*c*x)+-1//4*b*c^-4*e^2*arctan(c*x)+-1//12*b*c^-1*e^2*x^3+1//4*b*x*c^-3*e^2+b*d*e*c^-2*arctan(c*x)+-1*b*d*e*x*c^-1)
@test integrate(x^-2*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(-1*d^2*x^-1*(a+b*arctan(c*x))+1//3*e^2*x^3*(a+b*arctan(c*x))+b*c*d^2*log(x)+2*d*e*x*(a+b*arctan(c*x))+-1//6*b*c^-1*e^2*x^2+-1//6*b*c^-3*(-1*e^2+3*c^4*d^2+6*d*e*c^2)*log(1+c^2*x^2))
@test integrate(x^-3*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :((1/2)*e^2*x^2*(a+b*arctan(c*x))+-1//2*d^2*x^-2*(a+b*arctan(c*x))+(1/2)*b*c^-2*e^2*arctan(c*x)+2*a*d*e*log(x)+-1//2*b*c*d^2*x^-1+-1//2*b*x*c^-1*e^2+-1//2*b*c^2*d^2*arctan(c*x)+im*b*d*e*Polylogarithms.polylog(2,-1*im*c*x)+-1*im*b*d*e*Polylogarithms.polylog(2,im*c*x))
@test integrate(x^-4*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(x*e^2*(a+b*arctan(c*x))+-1//3*d^2*x^-3*(a+b*arctan(c*x))+-2*d*e*x^-1*(a+b*arctan(c*x))+-1//6*b*c*d^2*x^-2+1//6*b*c^-1*(-3*e^2+c^4*d^2+-6*d*e*c^2)*log(1+c^2*x^2)+-1//3*b*c*d*(-6*e+d*c^2)*log(x))
@test integrate(x^-5*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(a*e^2*log(x)+-1//4*d^2*x^-4*(a+b*arctan(c*x))+(1/2)*im*b*e^2*Polylogarithms.polylog(2,-1*im*c*x)+-1*d*e*x^-2*(a+b*arctan(c*x))+-1//2*im*b*e^2*Polylogarithms.polylog(2,im*c*x)+-1//12*b*c*d^2*x^-3+1//4*b*c^3*d^2*x^-1+1//4*b*c^4*d^2*arctan(c*x)+-1*b*c*d*e*x^-1+-1*b*d*e*c^2*arctan(c*x))
@test integrate(x^-6*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(-1*e^2*x^-1*(a+b*arctan(c*x))+-1//5*d^2*x^-5*(a+b*arctan(c*x))+-2//3*d*e*x^-3*(a+b*arctan(c*x))+-1//20*b*c*d^2*x^-4+-1//30*b*c*(15*e^2+3*c^4*d^2+-10*d*e*c^2)*log(1+c^2*x^2)+1//15*b*c*(15*e^2+3*c^4*d^2+-10*d*e*c^2)*log(x)+1//30*b*c*d*x^-2*(-10*e+3*d*c^2))
@test integrate(x^-7*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(-1//6*b*c*x^-1*(3*e^2+c^4*d^2+-3*d*e*c^2)+-1//6*b*d^-1*(-1*e+d*c^2)^3*arctan(c*x)+-1//6*d^-1*x^-6*(d+e*x^2)^3*(a+b*arctan(c*x))+-1//30*b*c*d^2*x^-5+1//18*b*c*d*x^-3*(-3*e+d*c^2))
@test integrate(x^-8*(d+e*x^2)^2*(a+b*arctan(c*x)), x) == :(-1//3*e^2*x^-3*(a+b*arctan(c*x))+-1//7*d^2*x^-7*(a+b*arctan(c*x))+-2//5*d*e*x^-5*(a+b*arctan(c*x))+-1//42*b*c*d^2*x^-6+-1//105*b*c^3*(35*e^2+15*c^4*d^2+-42*d*e*c^2)*log(x)+-1//210*b*c*x^-2*(35*e^2+15*c^4*d^2+-42*d*e*c^2)+1//210*b*c^3*(35*e^2+15*c^4*d^2+-42*d*e*c^2)*log(1+c^2*x^2)+1//140*b*c*d*x^-4*(-14*e+5*d*c^2))
@test integrate(x^3*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(1//10*e^-2*(d+e*x^2)^5*(a+b*arctan(c*x))+-1//8*d*e^-2*(d+e*x^2)^4*(a+b*arctan(c*x))+-1//90*b*c^-1*e^3*x^9+-1//120*b*c^-7*x^3*(-4*e^3+10*c^6*d^3+-20*e*c^4*d^2+15*d*c^2*e^2)+1//40*b*x*c^-9*(-4*e^3+10*c^6*d^3+-20*e*c^4*d^2+15*d*c^2*e^2)+-1//200*b*e*c^-5*x^5*(4*e^2+20*c^4*d^2+-15*d*e*c^2)+-1//280*b*c^-3*e^2*x^7*(-4*e+15*d*c^2)+1//40*b*c^-10*e^-2*(-1*e+d*c^2)^4*(4*e+d*c^2)*arctan(c*x))
@test integrate(x^2*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(1//3*d^3*x^3*(a+b*arctan(c*x))+1//9*e^3*x^9*(a+b*arctan(c*x))+-1//72*b*c^-1*e^3*x^8+-1//630*b*c^-7*x^2*(-35*e^3+105*c^6*d^3+-189*e*c^4*d^2+135*d*c^2*e^2)+1//630*b*c^-9*(-35*e^3+105*c^6*d^3+-189*e*c^4*d^2+135*d*c^2*e^2)*log(1+c^2*x^2)+3//5*e*d^2*x^5*(a+b*arctan(c*x))+3//7*d*e^2*x^7*(a+b*arctan(c*x))+-1//378*b*c^-3*e^2*x^6*(-7*e+27*d*c^2)+-1//1260*b*e*c^-5*x^4*(35*e^2+189*c^4*d^2+-135*d*e*c^2))
@test integrate(x*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(1//8*e^-1*(d+e*x^2)^4*(a+b*arctan(c*x))+-1//56*b*c^-1*e^3*x^7+-1//8*b*x*c^-7*(-1*e+2*d*c^2)*(e^2+2*c^4*d^2+-2*d*e*c^2)+-1//8*b*c^-8*e^-1*(-1*e+d*c^2)^4*arctan(c*x)+-1//24*b*e*c^-5*x^3*(e^2+6*c^4*d^2+-4*d*e*c^2)+-1//40*b*c^-3*e^2*x^5*(-1*e+4*d*c^2))
@test integrate((d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(x*d^3*(a+b*arctan(c*x))+1//7*e^3*x^7*(a+b*arctan(c*x))+e*d^2*x^3*(a+b*arctan(c*x))+-1//42*b*c^-1*e^3*x^6+-1//70*b*c^-7*(-5*e^3+35*c^6*d^3+-35*e*c^4*d^2+21*d*c^2*e^2)*log(1+c^2*x^2)+3//5*d*e^2*x^5*(a+b*arctan(c*x))+-1//70*b*e*c^-5*x^2*(5*e^2+35*c^4*d^2+-21*d*e*c^2)+-1//140*b*c^-3*e^2*x^4*(-5*e+21*d*c^2))
@test integrate(x^-1*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(a*d^3*log(x)+1//6*e^3*x^6*(a+b*arctan(c*x))+(1/2)*im*b*d^3*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*d^3*Polylogarithms.polylog(2,im*c*x)+-1//6*b*x*c^-5*e^3+-1//30*b*c^-1*e^3*x^5+1//6*b*c^-6*e^3*arctan(c*x)+1//18*b*c^-3*e^3*x^3+3//2*e*d^2*x^2*(a+b*arctan(c*x))+3//4*d*e^2*x^4*(a+b*arctan(c*x))+-3//2*b*e*x*c^-1*d^2+-3//4*b*d*c^-4*e^2*arctan(c*x)+-1//4*b*d*c^-1*e^2*x^3+3//2*b*e*c^-2*d^2*arctan(c*x)+3//4*b*d*x*c^-3*e^2)
@test integrate(x^-2*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(-1*d^3*x^-1*(a+b*arctan(c*x))+1//5*e^3*x^5*(a+b*arctan(c*x))+b*c*d^3*log(x)+d*e^2*x^3*(a+b*arctan(c*x))+3*e*x*d^2*(a+b*arctan(c*x))+-1//10*b*c^-5*(e^3+5*c^6*d^3+-5*d*c^2*e^2+15*e*c^4*d^2)*log(1+c^2*x^2)+-1//20*b*c^-1*e^3*x^4+-1//10*b*c^-3*e^2*x^2*(-1*e+5*d*c^2))
@test integrate(x^-3*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(-1//2*d^3*x^-2*(a+b*arctan(c*x))+1//4*e^3*x^4*(a+b*arctan(c*x))+3*a*e*d^2*log(x)+-1//2*b*c*d^3*x^-1+-1//2*b*c^2*d^3*arctan(c*x)+-1//4*b*c^-4*e^3*arctan(c*x)+-1//12*b*c^-1*e^3*x^3+1//4*b*x*c^-3*e^3+3//2*d*e^2*x^2*(a+b*arctan(c*x))+-3//2*im*b*e*d^2*Polylogarithms.polylog(2,im*c*x)+-3//2*b*d*x*c^-1*e^2+3//2*im*b*e*d^2*Polylogarithms.polylog(2,-1*im*c*x)+3//2*b*d*c^-2*e^2*arctan(c*x))
@test integrate(x^-4*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(-1//3*d^3*x^-3*(a+b*arctan(c*x))+1//3*e^3*x^3*(a+b*arctan(c*x))+-3*e*d^2*x^-1*(a+b*arctan(c*x))+3*d*x*e^2*(a+b*arctan(c*x))+-1//6*b*c*d^3*x^-2+-1//6*b*c^-1*e^3*x^2+-1//3*b*c*d^2*(-9*e+d*c^2)*log(x)+1//6*b*c^-3*(e+d*c^2)*(e^2+c^4*d^2+-10*d*e*c^2)*log(1+c^2*x^2))
@test integrate(x^-5*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :((1/2)*e^3*x^2*(a+b*arctan(c*x))+-1//4*d^3*x^-4*(a+b*arctan(c*x))+(1/2)*b*c^-2*e^3*arctan(c*x)+3*a*d*e^2*log(x)+-3//2*e*d^2*x^-2*(a+b*arctan(c*x))+-1//2*b*x*c^-1*e^3+-1//12*b*c*d^3*x^-3+1//4*b*c^3*d^3*x^-1+1//4*b*c^4*d^3*arctan(c*x)+-3//2*im*b*d*e^2*Polylogarithms.polylog(2,im*c*x)+-3//2*b*c*e*d^2*x^-1+-3//2*b*e*c^2*d^2*arctan(c*x)+3//2*im*b*d*e^2*Polylogarithms.polylog(2,-1*im*c*x))
@test integrate(x^-6*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(x*e^3*(a+b*arctan(c*x))+-1//5*d^3*x^-5*(a+b*arctan(c*x))+-1*e*d^2*x^-3*(a+b*arctan(c*x))+-3*d*e^2*x^-1*(a+b*arctan(c*x))+-1//10*b*c^-1*(5*e^3+c^6*d^3+-5*e*c^4*d^2+15*d*c^2*e^2)*log(1+c^2*x^2)+-1//20*b*c*d^3*x^-4+1//5*b*c*d*(15*e^2+c^4*d^2+-5*d*e*c^2)*log(x)+1//10*b*c*d^2*x^-2*(-5*e+d*c^2))
@test integrate(x^-7*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(a*e^3*log(x)+-1//6*d^3*x^-6*(a+b*arctan(c*x))+(1/2)*im*b*e^3*Polylogarithms.polylog(2,-1*im*c*x)+-3//2*d*e^2*x^-2*(a+b*arctan(c*x))+-3//4*e*d^2*x^-4*(a+b*arctan(c*x))+-1//2*im*b*e^3*Polylogarithms.polylog(2,im*c*x)+-1//6*b*c^5*d^3*x^-1+-1//6*b*c^6*d^3*arctan(c*x)+-1//30*b*c*d^3*x^-5+1//18*b*c^3*d^3*x^-3+-3//2*b*c*d*e^2*x^-1+-3//2*b*d*c^2*e^2*arctan(c*x)+-1//4*b*c*e*d^2*x^-3+3//4*b*e*c^3*d^2*x^-1+3//4*b*e*c^4*d^2*arctan(c*x))
@test integrate(x^-8*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(-1*e^3*x^-1*(a+b*arctan(c*x))+-1//7*d^3*x^-7*(a+b*arctan(c*x))+-1*d*e^2*x^-3*(a+b*arctan(c*x))+-3//5*e*d^2*x^-5*(a+b*arctan(c*x))+-1//35*b*c*(-35*e^3+5*c^6*d^3+-21*e*c^4*d^2+35*d*c^2*e^2)*log(x)+-1//42*b*c*d^3*x^-6+1//70*b*c*(-35*e^3+5*c^6*d^3+-21*e*c^4*d^2+35*d*c^2*e^2)*log(1+c^2*x^2)+-1//70*b*c*d*x^-2*(35*e^2+5*c^4*d^2+-21*d*e*c^2)+1//140*b*c*d^2*x^-4*(-21*e+5*d*c^2))
@test integrate(x^-9*(d+e*x^2)^3*(a+b*arctan(c*x)), x) == :(-1//8*d^-1*x^-8*(d+e*x^2)^4*(a+b*arctan(c*x))+-1//56*b*c*d^3*x^-7+1//8*b*d^-1*(-1*e+d*c^2)^4*arctan(c*x)+-1//24*b*c*d*x^-3*(6*e^2+c^4*d^2+-4*d*e*c^2)+1//8*b*c*x^-1*(-2*e+d*c^2)*(2*e^2+c^4*d^2+-2*d*e*c^2)+1//40*b*c*d^2*x^-5*(-4*e+d*c^2))
@test integrate((c+d*x^2)^4*arctan(a*x), x) == :(x*c^4*arctan(a*x)+-1//72*a^-1*d^4*x^8+-1//630*a^-9*(35*d^4+315*a^8*c^4+-420*d*a^6*c^3+-180*c*a^2*d^3+378*a^4*c^2*d^2)*log(1+a^2*x^2)+1//9*d^4*x^9*arctan(a*x)+-1//378*a^-3*d^3*x^6*(-7d+36*c*a^2)+-1//630*d*a^-7*x^2*(-35*d^3+420*a^6*c^3+-378*d*a^4*c^2+180*c*a^2*d^2)+-1//1260*a^-5*d^2*x^4*(35*d^2+378*a^4*c^2+-180*c*d*a^2)+4//3*d*c^3*x^3*arctan(a*x)+4//7*c*d^3*x^7*arctan(a*x)+6//5*c^2*d^2*x^5*arctan(a*x))
@test integrate(x^3*(d+e*x^2)^-1*(a+b*arctan(c*x)), x) == :((1/2)*e^-1*x^2*(a+b*arctan(c*x))+d*e^-2*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+(1/2)*b*c^-2*e^-1*arctan(c*x)+-1//2*b*x*c^-1*e^-1+-1//2*d*e^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*d*e^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//2*im*b*d*e^-2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+1//4*im*b*d*e^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*im*b*d*e^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x*(d+e*x^2)^-1*(a+b*arctan(c*x)), x) == :((1/2)*e^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*e^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*e^-1*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+(1/2)*im*b*e^-1*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//4*im*b*e^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*im*b*e^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^-1*(d+e*x^2)^-1*(a+b*arctan(c*x)), x) == :(a*d^-1*log(x)+d^-1*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1//2*d^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*d^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+(1/2)*im*b*d^-1*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*d^-1*Polylogarithms.polylog(2,im*c*x)+-1//2*im*b*d^-1*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+1//4*im*b*d^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*im*b*d^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^-3*(d+e*x^2)^-1*(a+b*arctan(c*x)), x) == :(-1//2*d^-1*x^-2*(a+b*arctan(c*x))+(1/2)*e*d^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*e*d^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*a*e*d^-2*log(x)+-1*e*d^-2*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1//2*b*c*d^-1*x^-1+-1//2*b*c^2*d^-1*arctan(c*x)+(1/2)*im*b*e*d^-2*Polylogarithms.polylog(2,im*c*x)+(1/2)*im*b*e*d^-2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//2*im*b*e*d^-2*Polylogarithms.polylog(2,-1*im*c*x)+-1//4*im*b*e*d^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*im*b*e*d^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^2*(d+e*x^2)^-1*(a+b*arctan(c*x)), x) == :(a*x*e^-1+b*x*e^-1*arctan(c*x)+-1*a*d^(1/2)*e^-3//2*arctan(x*d^-1//2*e^(1/2))+-1//2*b*c^-1*e^-1*log(1+c^2*x^2)+-1//4*im*b*e^-3//2*(-1d)^(1/2)*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+im*c*x))+-1//4*im*b*e^-3//2*(-1d)^(1/2)*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+-1*im*c*x))+1//4*im*b*e^-3//2*(-1d)^(1/2)*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+c*x))+1//4*im*b*e^-3//2*(-1d)^(1/2)*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+-1*c*x))+-1//4*im*b*e^-3//2*(-1d)^(1/2)*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+-1*im*c*x)+-1//4*im*b*e^-3//2*(-1d)^(1/2)*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+im*c*x)+1//4*im*b*e^-3//2*(-1d)^(1/2)*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+im*c*x)+1//4*im*b*e^-3//2*(-1d)^(1/2)*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+-1*im*c*x))
@test integrate((d+e*x^2)^-1*(a+b*arctan(c*x)), x) == :(a*d^-1//2*e^-1//2*arctan(x*d^-1//2*e^(1/2))+-1//4*im*b*e^-1//2*(-1d)^-1//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+im*c*x))+-1//4*im*b*e^-1//2*(-1d)^-1//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+-1*im*c*x))+1//4*im*b*e^-1//2*(-1d)^-1//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+c*x))+1//4*im*b*e^-1//2*(-1d)^-1//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+-1*c*x))+-1//4*im*b*e^-1//2*(-1d)^-1//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+-1*im*c*x)+-1//4*im*b*e^-1//2*(-1d)^-1//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+im*c*x)+1//4*im*b*e^-1//2*(-1d)^-1//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+im*c*x)+1//4*im*b*e^-1//2*(-1d)^-1//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+-1*im*c*x))
@test integrate(x^-2*(d+e*x^2)^-1*(a+b*arctan(c*x)), x) == :(-1*d^-1*x^-1*(a+b*arctan(c*x))+b*c*d^-1*log(x)+-1*a*d^-3//2*e^(1/2)*arctan(x*d^-1//2*e^(1/2))+-1//2*b*c*d^-1*log(1+c^2*x^2)+-1//4*im*b*e^(1/2)*(-1d)^-3//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+im*c*x))+-1//4*im*b*e^(1/2)*(-1d)^-3//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+-1*im*c*x))+1//4*im*b*e^(1/2)*(-1d)^-3//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+c*x))+1//4*im*b*e^(1/2)*(-1d)^-3//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+-1*c*x))+-1//4*im*b*e^(1/2)*(-1d)^-3//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+-1*im*c*x)+-1//4*im*b*e^(1/2)*(-1d)^-3//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+im*c*x)+1//4*im*b*e^(1/2)*(-1d)^-3//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+im*c*x)+1//4*im*b*e^(1/2)*(-1d)^-3//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+-1*im*c*x))
@test integrate(x^3*(d+e*x^2)^-2*(a+b*arctan(c*x)), x) == :((1/2)*e^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*e^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*e^-2*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+(1/2)*im*b*e^-2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+(1/2)*d*e^-2*(d+e*x^2)^-1*(a+b*arctan(c*x))+-1//4*im*b*e^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*im*b*e^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+b*c*d^(1/2)*e^-3//2*(-2*e+2*d*c^2)^-1*arctan(x*d^-1//2*e^(1/2))+-1*b*d*c^2*e^-2*(-2*e+2*d*c^2)^-1*arctan(c*x))
@test integrate(x*(d+e*x^2)^-2*(a+b*arctan(c*x)), x) == :(-1//2*e^-1*(d+e*x^2)^-1*(a+b*arctan(c*x))+b*c^2*e^-1*(-2*e+2*d*c^2)^-1*arctan(c*x)+-1//2*b*c*d^-1//2*e^-1//2*(-1*e+d*c^2)^-1*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^-1*(d+e*x^2)^-2*(a+b*arctan(c*x)), x) == :(a*d^-2*log(x)+d^-2*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+(1/2)*d^-1*(d+e*x^2)^-1*(a+b*arctan(c*x))+-1//2*d^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*d^-2*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+(1/2)*im*b*d^-2*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*d^-2*Polylogarithms.polylog(2,im*c*x)+-1//2*im*b*d^-2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+1//4*im*b*d^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*im*b*d^-2*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//2*b*c^2*d^-1*(-1*e+d*c^2)^-1*arctan(c*x)+(1/2)*b*c*d^-3//2*e^(1/2)*(-1*e+d*c^2)^-1*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^-3*(d+e*x^2)^-2*(a+b*arctan(c*x)), x) == :(-1//2*d^-2*x^-2*(a+b*arctan(c*x))+e*d^-3*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+e*d^-3*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-2*a*e*d^-3*log(x)+-2*e*d^-3*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1//2*b*c*d^-2*x^-1+-1//2*b*c^2*d^-2*arctan(c*x)+-1//2*e*d^-2*(d+e*x^2)^-1*(a+b*arctan(c*x))+im*b*e*d^-3*Polylogarithms.polylog(2,im*c*x)+im*b*e*d^-3*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1*im*b*e*d^-3*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*e*d^-3*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*im*b*e*d^-3*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+(1/2)*b*e*c^2*d^-2*(-1*e+d*c^2)^-1*arctan(c*x)+-1//2*b*c*d^-5//2*e^3//2*(-1*e+d*c^2)^-1*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^2*(d+e*x^2)^-2*(a+b*arctan(c*x)), x) == :(a*d^-1//2*e^-3//2*arctan(x*d^-1//2*e^(1/2))+-1//2*x*e^-1*(d+e*x^2)^-1*(a+b*arctan(c*x))+-1//2*d^-1//2*e^-3//2*(a+b*arctan(c*x))*arctan(x*d^-1//2*e^(1/2))+b*c*e^-1*(-4*e+4*d*c^2)^-1*log(1+c^2*x^2)+-1*b*c*e^-1*(-4*e+4*d*c^2)^-1*log(d+e*x^2)+-1//4*im*b*e^-3//2*(-1d)^-1//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+im*c*x))+-1//4*im*b*e^-3//2*(-1d)^-1//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+-1*im*c*x))+1//4*im*b*e^-3//2*(-1d)^-1//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+c*x))+1//4*im*b*e^-3//2*(-1d)^-1//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+-1*c*x))+-1//4*im*b*e^-3//2*(-1d)^-1//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+-1*im*c*x)+-1//4*im*b*e^-3//2*(-1d)^-1//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+im*c*x)+1//4*im*b*e^-3//2*(-1d)^-1//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+im*c*x)+1//4*im*b*e^-3//2*(-1d)^-1//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+-1*im*c*x)+-1//8*im*b*c*d^-1//2*e^-3//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+-1//8*im*b*c*d^-1//2*e^-3//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+1//8*im*b*c*d^-1//2*e^-3//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+1//8*im*b*c*d^-1//2*e^-3//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+-1//8*im*b*c*d^-1//2*e^-3//2*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2))+-1//8*im*b*c*d^-1//2*e^-3//2*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2))+1//8*im*b*c*d^-1//2*e^-3//2*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2))+1//8*im*b*c*d^-1//2*e^-3//2*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2)))
@test integrate((d+e*x^2)^-2*(a+b*arctan(c*x)), x) == :((1/2)*x*d^-1*(d+e*x^2)^-1*(a+b*arctan(c*x))+(1/2)*d^-3//2*e^-1//2*(a+b*arctan(c*x))*arctan(x*d^-1//2*e^(1/2))+-1//4*b*c*d^-1*(-1*e+d*c^2)^-1*log(1+c^2*x^2)+1//4*b*c*d^-1*(-1*e+d*c^2)^-1*log(d+e*x^2)+-1//8*im*b*c*d^-3//2*e^-1//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+-1//8*im*b*c*d^-3//2*e^-1//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+1//8*im*b*c*d^-3//2*e^-1//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+1//8*im*b*c*d^-3//2*e^-1//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+-1//8*im*b*c*d^-3//2*e^-1//2*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2))+-1//8*im*b*c*d^-3//2*e^-1//2*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2))+1//8*im*b*c*d^-3//2*e^-1//2*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2))+1//8*im*b*c*d^-3//2*e^-1//2*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2)))
@test integrate(x^-2*(d+e*x^2)^-2*(a+b*arctan(c*x)), x) == :(-1*d^-2*x^-1*(a+b*arctan(c*x))+b*c*d^-2*log(x)+-1*a*d^-5//2*e^(1/2)*arctan(x*d^-1//2*e^(1/2))+-1//2*b*c*d^-2*log(1+c^2*x^2)+-1//2*d^-5//2*e^(1/2)*(a+b*arctan(c*x))*arctan(x*d^-1//2*e^(1/2))+-1//2*e*x*d^-2*(d+e*x^2)^-1*(a+b*arctan(c*x))+-1//4*im*b*e^(1/2)*(-1d)^-5//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+c*x))+-1//4*im*b*e^(1/2)*(-1d)^-5//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+-1*c*x))+1//4*im*b*e^(1/2)*(-1d)^-5//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+im*c*x))+1//4*im*b*e^(1/2)*(-1d)^-5//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+-1*im*c*x))+-1//4*im*b*e^(1/2)*(-1d)^-5//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+im*c*x)+-1//4*im*b*e^(1/2)*(-1d)^-5//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+-1*im*c*x)+-1//4*b*c*e*d^-2*(-1*e+d*c^2)^-1*log(d+e*x^2)+1//4*im*b*e^(1/2)*(-1d)^-5//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+-1*im*c*x)+1//4*im*b*e^(1/2)*(-1d)^-5//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+im*c*x)+1//4*b*c*e*d^-2*(-1*e+d*c^2)^-1*log(1+c^2*x^2)+-1//8*im*b*c*d^-5//2*e^(1/2)*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+-1//8*im*b*c*d^-5//2*e^(1/2)*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+1//8*im*b*c*d^-5//2*e^(1/2)*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+1//8*im*b*c*d^-5//2*e^(1/2)*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+-1//8*im*b*c*d^-5//2*e^(1/2)*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2))+-1//8*im*b*c*d^-5//2*e^(1/2)*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2))+1//8*im*b*c*d^-5//2*e^(1/2)*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2))+1//8*im*b*c*d^-5//2*e^(1/2)*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2)))
@test integrate(x^5*(d+e*x^2)^-3*(a+b*arctan(c*x)), x) == :((1/2)*e^-3*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*e^-3*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*e^-3*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+d*e^-3*(d+e*x^2)^-1*(a+b*arctan(c*x))+(1/2)*im*b*e^-3*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//4*im*b*e^-3*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*im*b*e^-3*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//4*d^2*e^-3*(d+e*x^2)^-2*(a+b*arctan(c*x))+b*c*d^(1/2)*e^-5//2*(-1*e+d*c^2)^-1*arctan(x*d^-1//2*e^(1/2))+-1*b*d*c^2*e^-3*(-1*e+d*c^2)^-1*arctan(c*x)+1//4*b*c^4*d^2*e^-3*(-1*e+d*c^2)^-2*arctan(c*x)+-1*b*c*d*x*e^-2*(d+e*x^2)^-1*(-8*e+8*d*c^2)^-1+-1//8*b*c*d^(1/2)*e^-5//2*(-1*e+d*c^2)^-2*(-1*e+3*d*c^2)*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^3*(d+e*x^2)^-3*(a+b*arctan(c*x)), x) == :(-1//4*b*d^-1*(-1*e+d*c^2)^-2*arctan(c*x)+1//4*d^-1*x^4*(d+e*x^2)^-2*(a+b*arctan(c*x))+b*c*x*e^-1*(d+e*x^2)^-1*(-8*e+8*d*c^2)^-1+-1//8*b*c*d^-1//2*e^-3//2*(-1*e+d*c^2)^-2*(-3*e+d*c^2)*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x*(d+e*x^2)^-3*(a+b*arctan(c*x)), x) == :(-1//4*e^-1*(d+e*x^2)^-2*(a+b*arctan(c*x))+1//4*b*c^4*e^-1*(-1*e+d*c^2)^-2*arctan(c*x)+-1//8*b*c*x*d^-1*(d+e*x^2)^-1*(-1*e+d*c^2)^-1+-1//8*b*c*d^-3//2*e^-1//2*(-1*e+d*c^2)^-2*(-1*e+3*d*c^2)*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^-1*(d+e*x^2)^-3*(a+b*arctan(c*x)), x) == :(a*d^-3*log(x)+d^-3*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+(1/2)*d^-2*(d+e*x^2)^-1*(a+b*arctan(c*x))+-1//2*d^-3*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*d^-3*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+1//4*d^-1*(d+e*x^2)^-2*(a+b*arctan(c*x))+(1/2)*im*b*d^-3*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*d^-3*Polylogarithms.polylog(2,im*c*x)+-1//2*im*b*d^-3*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+1//4*im*b*d^-3*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*im*b*d^-3*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//2*b*c^2*d^-2*(-1*e+d*c^2)^-1*arctan(c*x)+-1//4*b*c^4*d^-1*(-1*e+d*c^2)^-2*arctan(c*x)+(1/2)*b*c*d^-5//2*e^(1/2)*(-1*e+d*c^2)^-1*arctan(x*d^-1//2*e^(1/2))+1//8*b*c*e*x*d^-2*(d+e*x^2)^-1*(-1*e+d*c^2)^-1+1//8*b*c*d^-5//2*e^(1/2)*(-1*e+d*c^2)^-2*(-1*e+3*d*c^2)*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^-3*(d+e*x^2)^-3*(a+b*arctan(c*x)), x) == :(-1//2*d^-3*x^-2*(a+b*arctan(c*x))+-1*e*d^-3*(d+e*x^2)^-1*(a+b*arctan(c*x))+-3*a*e*d^-4*log(x)+-3*e*d^-4*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1//2*b*c*d^-3*x^-1+-1//2*b*c^2*d^-3*arctan(c*x)+-1//4*e*d^-2*(d+e*x^2)^-2*(a+b*arctan(c*x))+3//2*e*d^-4*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+3//2*e*d^-4*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-3//2*im*b*e*d^-4*Polylogarithms.polylog(2,-1*im*c*x)+-3//4*im*b*e*d^-4*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-3//4*im*b*e*d^-4*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+3//2*im*b*e*d^-4*Polylogarithms.polylog(2,im*c*x)+3//2*im*b*e*d^-4*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+b*e*c^2*d^-3*(-1*e+d*c^2)^-1*arctan(c*x)+-1*b*c*d^-7//2*e^3//2*(-1*e+d*c^2)^-1*arctan(x*d^-1//2*e^(1/2))+1//4*b*e*c^4*d^-2*(-1*e+d*c^2)^-2*arctan(c*x)+-1//8*b*c*x*d^-3*e^2*(d+e*x^2)^-1*(-1*e+d*c^2)^-1+-1//8*b*c*d^-7//2*e^3//2*(-1*e+d*c^2)^-2*(-1*e+3*d*c^2)*arctan(x*d^-1//2*e^(1/2)))
@test integrate(x^2*(d+e*x^2)^-3*(a+b*arctan(c*x)), x) == :(-1//4*x*e^-1*(d+e*x^2)^-2*(a+b*arctan(c*x))+1//8*d^-3//2*e^-3//2*(a+b*arctan(c*x))*arctan(x*d^-1//2*e^(1/2))+b*c*e^-1*(d+e*x^2)^-1*(-8*e+8*d*c^2)^-1+1//8*x*d^-1*e^-1*(d+e*x^2)^-1*(a+b*arctan(c*x))+-1//4*b*c*d^-1*e^-1*(-1*e+d*c^2)^-1*log(1+c^2*x^2)+1//4*b*c*d^-1*e^-1*(-1*e+d*c^2)^-1*log(d+e*x^2)+-1//16*b*c*d^-1*e^-1*(-1*e+d*c^2)^-2*(-3*e+5*d*c^2)*log(d+e*x^2)+-1//32*im*b*c*d^-3//2*e^-3//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+-1//32*im*b*c*d^-3//2*e^-3//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+1//16*b*c*d^-1*e^-1*(-1*e+d*c^2)^-2*(-3*e+5*d*c^2)*log(1+c^2*x^2)+1//32*im*b*c*d^-3//2*e^-3//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+1//32*im*b*c*d^-3//2*e^-3//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+-1//32*im*b*c*d^-3//2*e^-3//2*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2))+-1//32*im*b*c*d^-3//2*e^-3//2*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2))+1//32*im*b*c*d^-3//2*e^-3//2*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2))+1//32*im*b*c*d^-3//2*e^-3//2*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2)))
@test integrate((d+e*x^2)^-3*(a+b*arctan(c*x)), x) == :(1//4*x*d^-1*(d+e*x^2)^-2*(a+b*arctan(c*x))+1//8*d^-5//2*e^-1//2*(3a+3*b*arctan(c*x))*arctan(x*d^-1//2*e^(1/2))+3//8*x*d^-2*(d+e*x^2)^-1*(a+b*arctan(c*x))+-1//8*b*c*d^-1*(d+e*x^2)^-1*(-1*e+d*c^2)^-1+-1//16*b*c*d^-2*(-1*e+d*c^2)^-2*(-3*e+5*d*c^2)*log(1+c^2*x^2)+1//16*b*c*d^-2*(-1*e+d*c^2)^-2*(-3*e+5*d*c^2)*log(d+e*x^2)+-3//32*im*b*c*d^-5//2*e^-1//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+-3//32*im*b*c*d^-5//2*e^-1//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+3//32*im*b*c*d^-5//2*e^-1//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+3//32*im*b*c*d^-5//2*e^-1//2*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+-3//32*im*b*c*d^-5//2*e^-1//2*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2))+-3//32*im*b*c*d^-5//2*e^-1//2*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2))+3//32*im*b*c*d^-5//2*e^-1//2*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2))+3//32*im*b*c*d^-5//2*e^-1//2*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2)))
@test integrate(x^-2*(d+e*x^2)^-3*(a+b*arctan(c*x)), x) == :(-1*d^-3*x^-1*(a+b*arctan(c*x))+b*c*d^-3*log(x)+-1*a*d^-7//2*e^(1/2)*arctan(x*d^-1//2*e^(1/2))+-7//8*d^-7//2*e^(1/2)*(a+b*arctan(c*x))*arctan(x*d^-1//2*e^(1/2))+-1//2*b*c*d^-3*log(1+c^2*x^2)+-7//8*e*x*d^-3*(d+e*x^2)^-1*(a+b*arctan(c*x))+-1//4*im*b*e^(1/2)*(-1d)^-7//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+im*c*x))+-1//4*im*b*e^(1/2)*(-1d)^-7//2*Polylogarithms.polylog(2,e^(1/2)*(e^(1/2)+im*c*(-1d)^(1/2))^-1*(1+-1*im*c*x))+-1//4*e*x*d^-2*(d+e*x^2)^-2*(a+b*arctan(c*x))+1//4*im*b*e^(1/2)*(-1d)^-7//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+c*x))+1//4*im*b*e^(1/2)*(-1d)^-7//2*Polylogarithms.polylog(2,e^(1/2)*(im*e^(1/2)+c*(-1d)^(1/2))^-1*(im+-1*c*x))+-1//4*im*b*e^(1/2)*(-1d)^-7//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+-1*im*c*x)+-1//4*im*b*e^(1/2)*(-1d)^-7//2*log(c*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+im*c*x)+-1//4*b*c*e*d^-3*(-1*e+d*c^2)^-1*log(d+e*x^2)+1//4*im*b*e^(1/2)*(-1d)^-7//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))*log(1+im*c*x)+1//4*im*b*e^(1/2)*(-1d)^-7//2*log(c*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))*log(1+-1*im*c*x)+1//4*b*c*e*d^-3*(-1*e+d*c^2)^-1*log(1+c^2*x^2)+1//8*b*c*e*d^-2*(d+e*x^2)^-1*(-1*e+d*c^2)^-1+-7//32*im*b*c*d^-7//2*e^(1/2)*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+-7//32*im*b*c*d^-7//2*e^(1/2)*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(d^(1/2)*(-1*c^2)^(1/2)+-1*im*e^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+-1//16*b*c*e*d^-3*(-1*e+d*c^2)^-2*(-3*e+5*d*c^2)*log(d+e*x^2)+1//16*b*c*e*d^-3*(-1*e+d*c^2)^-2*(-3*e+5*d*c^2)*log(1+c^2*x^2)+7//32*im*b*c*d^-7//2*e^(1/2)*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+im*x*e^(1/2)))+7//32*im*b*c*d^-7//2*e^(1/2)*(-1*c^2)^-1//2*Polylogarithms.polylog(2,(-1*c^2)^(1/2)*(im*e^(1/2)+d^(1/2)*(-1*c^2)^(1/2))^-1*(d^(1/2)+-1*im*x*e^(1/2)))+-7//32*im*b*c*d^-7//2*e^(1/2)*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2))+-7//32*im*b*c*d^-7//2*e^(1/2)*(-1*c^2)^-1//2*log(e^(1/2)*(e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2))+7//32*im*b*c*d^-7//2*e^(1/2)*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+x*(-1*c^2)^(1/2)))*log(1+-1*im*x*d^-1//2*e^(1/2))+7//32*im*b*c*d^-7//2*e^(1/2)*(-1*c^2)^-1//2*log(-1*e^(1/2)*(-1*e^(1/2)+im*d^(1/2)*(-1*c^2)^(1/2))^-1*(1+-1*x*(-1*c^2)^(1/2)))*log(1+im*x*d^-1//2*e^(1/2)))
@test integrate(x*(d+e*x^2)^(1/2)*(a+b*arctan(c*x)), x) == :(1//3*e^-1*(d+e*x^2)^3//2*(a+b*arctan(c*x))+-1//6*b*x*c^-1*(d+e*x^2)^(1/2)+-1//3*b*c^-3*e^-1*(-1*e+d*c^2)^3//2*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2))+-1//6*b*c^-3*e^-1//2*(-2*e+3*d*c^2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2))
@test integrate(x^-4*(d+e*x^2)^(1/2)*(a+b*arctan(c*x)), x) == :(-1//3*b*d^-1*(-1*e+d*c^2)^3//2*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+-1//3*d^-1*x^-3*(d+e*x^2)^3//2*(a+b*arctan(c*x))+-1//6*b*c*x^-2*(d+e*x^2)^(1/2)+1//6*b*c*d^-1//2*(-3*e+2*d*c^2)*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x^3*(d+e*x^2)^3//2*(a+b*arctan(c*x)), x) == :(1//7*e^-2*(d+e*x^2)^7//2*(a+b*arctan(c*x))+-1//5*d*e^-2*(d+e*x^2)^5//2*(a+b*arctan(c*x))+-1//42*b*x*c^-1*e^-1*(d+e*x^2)^5//2+1//560*b*c^-7*e^-3//2*(80*e^3+35*c^6*d^3+-168*d*c^2*e^2+70*e*c^4*d^2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//840*b*x*c^-3*e^-1*(d+e*x^2)^3//2*(-30*e+13*d*c^2)+1//35*b*c^-7*e^-2*(-1*e+d*c^2)^5//2*(5*e+2*d*c^2)*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2))+1//560*b*x*c^-5*e^-1*(d+e*x^2)^(1/2)*(-40*e^2+3*c^4*d^2+54*d*e*c^2))
@test integrate(x*(d+e*x^2)^3//2*(a+b*arctan(c*x)), x) == :(1//5*e^-1*(d+e*x^2)^5//2*(a+b*arctan(c*x))+-1//20*b*x*c^-1*(d+e*x^2)^3//2+-1//5*b*c^-5*e^-1*(-1*e+d*c^2)^5//2*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2))+-1//40*b*x*c^-3*(d+e*x^2)^(1/2)*(-4*e+7*d*c^2)+-1//40*b*c^-5*e^-1//2*(8*e^2+15*c^4*d^2+-20*d*e*c^2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2))
@test integrate(x^-6*(d+e*x^2)^3//2*(a+b*arctan(c*x)), x) == :(-1//5*d^-1*x^-5*(d+e*x^2)^5//2*(a+b*arctan(c*x))+-1//20*b*c*x^-4*(d+e*x^2)^3//2+1//5*b*d^-1*(-1*e+d*c^2)^5//2*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+-1//40*b*c*d^-1//2*(15*e^2+8*c^4*d^2+-20*d*e*c^2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+1//40*b*c*x^-2*(d+e*x^2)^(1/2)*(-7*e+4*d*c^2))
@test integrate(x^3*(d+e*x^2)^5//2*(a+b*arctan(c*x)), x) == :(1//9*e^-2*(d+e*x^2)^9//2*(a+b*arctan(c*x))+-1//7*d*e^-2*(d+e*x^2)^7//2*(a+b*arctan(c*x))+-1//72*b*x*c^-1*e^-1*(d+e*x^2)^7//2+1//8064*b*c^-9*e^-3//2*(-896*e^4+315*c^8*d^4+-3024*c^4*d^2*e^2+840*e*c^6*d^3+2880*d*c^2*e^3)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//3024*b*x*c^-3*e^-1*(d+e*x^2)^5//2*(-56*e+33*d*c^2)+-1//12096*b*x*c^-5*e^-1*(d+e*x^2)^3//2*(336*e^2+69*c^4*d^2+-520*d*e*c^2)+1//63*b*c^-9*e^-2*(-1*e+d*c^2)^7//2*(7*e+2*d*c^2)*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2))+1//8064*b*x*c^-7*e^-1*(d+e*x^2)^(1/2)*(448*e^3+59*c^6*d^3+-1104*d*c^2*e^2+712*e*c^4*d^2))
@test integrate(x*(d+e*x^2)^5//2*(a+b*arctan(c*x)), x) == :(1//7*e^-1*(d+e*x^2)^7//2*(a+b*arctan(c*x))+-1//42*b*x*c^-1*(d+e*x^2)^5//2+-1//7*b*c^-7*e^-1*(-1*e+d*c^2)^7//2*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2))+-1//112*b*x*c^-5*(d+e*x^2)^(1/2)*(8*e^2+19*c^4*d^2+-22*d*e*c^2)+-1//112*b*c^-7*e^-1//2*(-16*e^3+35*c^6*d^3+-70*e*c^4*d^2+56*d*c^2*e^2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//168*b*x*c^-3*(d+e*x^2)^3//2*(-6*e+11*d*c^2))
@test integrate(x^3*(d+e*x^2)^-1//2*(a+b*arctan(c*x)), x) == :(1//3*e^-2*(d+e*x^2)^3//2*(a+b*arctan(c*x))+-1*d*e^-2*(d+e*x^2)^(1/2)*(a+b*arctan(c*x))+-1//6*b*x*c^-1*e^-1*(d+e*x^2)^(1/2)+1//6*b*c^-3*e^-3//2*(2*e+3*d*c^2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+1//3*b*c^-3*e^-2*(-1*e+d*c^2)^(1/2)*(e+2*d*c^2)*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2)))
@test integrate(x*(d+e*x^2)^-1//2*(a+b*arctan(c*x)), x) == :(e^-1*(d+e*x^2)^(1/2)*(a+b*arctan(c*x))+-1*b*c^-1*e^-1//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1*b*c^-1*e^-1*(-1*e+d*c^2)^(1/2)*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2)))
@test integrate(x^-2*(d+e*x^2)^-1//2*(a+b*arctan(c*x)), x) == :(b*d^-1*(-1*e+d*c^2)^(1/2)*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+-1*b*c*d^-1//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1*d^-1*x^-1*(d+e*x^2)^(1/2)*(a+b*arctan(c*x)))
@test integrate(x^-4*(d+e*x^2)^-1//2*(a+b*arctan(c*x)), x) == :(-1//3*d^-1*x^-3*(d+e*x^2)^(1/2)*(a+b*arctan(c*x))+-1//3*b*d^-2*(-1*e+d*c^2)^(1/2)*(2*e+d*c^2)*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+-1//6*b*c*d^-1*x^-2*(d+e*x^2)^(1/2)+1//6*b*c*d^-3//2*(3*e+2*d*c^2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+2//3*e*d^-2*x^-1*(d+e*x^2)^(1/2)*(a+b*arctan(c*x)))
@test integrate(x^3*(d+e*x^2)^-3//2*(a+b*arctan(c*x)), x) == :(e^-2*(d+e*x^2)^(1/2)*(a+b*arctan(c*x))+d*e^-2*(d+e*x^2)^-1//2*(a+b*arctan(c*x))+-1*b*c^-1*e^-3//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1*b*c^-1*e^-2*(-1*e+d*c^2)^-1//2*(-1*e+2*d*c^2)*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2)))
@test integrate(x*(d+e*x^2)^-3//2*(a+b*arctan(c*x)), x) == :(-1*e^-1*(d+e*x^2)^-1//2*(a+b*arctan(c*x))+b*c*e^-1*(-1*e+d*c^2)^-1//2*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2)))
@test integrate((d+e*x^2)^-3//2*(a+b*arctan(c*x)), x) == :(b*d^-1*(-1*e+d*c^2)^-1//2*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+x*d^-1*(d+e*x^2)^-1//2*(a+b*arctan(c*x)))
@test integrate(x^-2*(d+e*x^2)^-3//2*(a+b*arctan(c*x)), x) == :(-1*b*c*d^-3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1*d^-1*x^-1*(d+e*x^2)^-1//2*(a+b*arctan(c*x))+b*d^-2*(-1*e+d*c^2)^-1//2*(-2*e+d*c^2)*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+-2*e*x*d^-2*(d+e*x^2)^-1//2*(a+b*arctan(c*x)))
@test integrate(x^-4*(d+e*x^2)^-3//2*(a+b*arctan(c*x)), x) == :(-1//3*d^-1*x^-3*(d+e*x^2)^-1//2*(a+b*arctan(c*x))+-1//3*b*d^-3*(-1*e+d*c^2)^-1//2*(-8*e^2+c^4*d^2+4*d*e*c^2)*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+-1//6*b*c*d^-2*x^-2*(d+e*x^2)^(1/2)+1//3*b*c*d^-5//2*(4*e+d*c^2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+1//6*b*c*e*d^-5//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+4//3*e*d^-2*x^-1*(d+e*x^2)^-1//2*(a+b*arctan(c*x))+8//3*x*d^-3*e^2*(d+e*x^2)^-1//2*(a+b*arctan(c*x)))
@test integrate(x^3*(d+e*x^2)^-5//2*(a+b*arctan(c*x)), x) == :(-1*e^-2*(d+e*x^2)^-1//2*(a+b*arctan(c*x))+1//3*d*e^-2*(d+e*x^2)^-3//2*(a+b*arctan(c*x))+b*c*x*e^-1*(d+e*x^2)^-1//2*(-3*e+3*d*c^2)^-1+1//3*b*c*e^-2*(-1*e+d*c^2)^-3//2*(-3*e+2*d*c^2)*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2)))
@test integrate(x^2*(d+e*x^2)^-5//2*(a+b*arctan(c*x)), x) == :(-1//3*b*d^-1*(-1*e+d*c^2)^-3//2*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+1//3*d^-1*x^3*(d+e*x^2)^-3//2*(a+b*arctan(c*x))+b*c*e^-1*(d+e*x^2)^-1//2*(-3*e+3*d*c^2)^-1)
@test integrate(x*(d+e*x^2)^-5//2*(a+b*arctan(c*x)), x) == :(-1//3*e^-1*(d+e*x^2)^-3//2*(a+b*arctan(c*x))+1//3*b*c^3*e^-1*(-1*e+d*c^2)^-3//2*arctan(x*(d+e*x^2)^-1//2*(-1*e+d*c^2)^(1/2))+-1//3*b*c*x*d^-1*(d+e*x^2)^-1//2*(-1*e+d*c^2)^-1)
@test integrate((d+e*x^2)^-5//2*(a+b*arctan(c*x)), x) == :(1//3*x*d^-1*(d+e*x^2)^-3//2*(a+b*arctan(c*x))+2//3*x*d^-2*(d+e*x^2)^-1//2*(a+b*arctan(c*x))+-1//3*b*c*d^-1*(d+e*x^2)^-1//2*(-1*e+d*c^2)^-1+1//3*b*d^-2*(-1*e+d*c^2)^-3//2*(-2*e+3*d*c^2)*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2))
@test integrate(x^-2*(d+e*x^2)^-5//2*(a+b*arctan(c*x)), x) == :(b*c*d^-2*(d+e*x^2)^-1//2+-1*b*c*d^-5//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1*d^-1*x^-1*(d+e*x^2)^-3//2*(a+b*arctan(c*x))+-8//3*b*e*c^-1*d^-3*(d+e*x^2)^-1//2+-8//3*e*x*d^-3*(d+e*x^2)^-1//2*(a+b*arctan(c*x))+-4//3*e*x*d^-2*(d+e*x^2)^-3//2*(a+b*arctan(c*x))+1//3*b*d^-3*(-1*e+d*c^2)^-3//2*(8*e^2+3*c^4*d^2+-12*d*e*c^2)*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+-1//3*b*c^-1*d^-3*(d+e*x^2)^-1//2*(-1*e+d*c^2)^-1*(8*e^2+3*c^4*d^2+-12*d*e*c^2))
@test integrate(x^-4*(d+e*x^2)^-5//2*(a+b*arctan(c*x)), x) == :(-1//3*d^-1*x^-3*(d+e*x^2)^-3//2*(a+b*arctan(c*x))+(1/2)*b*c*e*d^-7//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+2*e*d^-2*x^-1*(d+e*x^2)^-3//2*(a+b*arctan(c*x))+-1//2*b*c*e*d^-3*(d+e*x^2)^-1//2+-1//3*b*c*d^-3*(d+e*x^2)^-1//2*(6*e+d*c^2)+-1//6*b*c*d^-2*x^-2*(d+e*x^2)^-1//2+1//3*b*c*d^-7//2*(6*e+d*c^2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+8//3*x*d^-3*e^2*(d+e*x^2)^-3//2*(a+b*arctan(c*x))+16//3*b*c^-1*d^-4*e^2*(d+e*x^2)^-1//2+16//3*x*d^-4*e^2*(d+e*x^2)^-1//2*(a+b*arctan(c*x))+-1//3*b*d^-4*(-1*e+d*c^2)^-3//2*(-2*e+d*c^2)*(-8*e^2+c^4*d^2+8*d*e*c^2)*arctanh(c*(d+e*x^2)^(1/2)*(-1*e+d*c^2)^-1//2)+1//3*b*c^-1*d^-4*(d+e*x^2)^-1//2*(-1*e+d*c^2)^-1*(-2*e+d*c^2)*(-8*e^2+c^4*d^2+8*d*e*c^2))
@test integrate((c+d*x^2)^-7//2*arctan(a*x), x) == :(-1//15*a*c^-1*(c+d*x^2)^-3//2*(-1d+c*a^2)^-1+1//5*x*c^-1*(c+d*x^2)^-5//2*arctan(a*x)+1//15*c^-3*(-1d+c*a^2)^-5//2*(8*d^2+15*a^4*c^2+-20*c*d*a^2)*arctanh(a*(c+d*x^2)^(1/2)*(-1d+c*a^2)^-1//2)+4//15*x*c^-2*(c+d*x^2)^-3//2*arctan(a*x)+8//15*x*c^-3*(c+d*x^2)^-1//2*arctan(a*x)+-1//15*a*c^-2*(c+d*x^2)^-1//2*(-1d+c*a^2)^-2*(-4d+7*c*a^2))
@test integrate((c+d*x^2)^-9//2*arctan(a*x), x) == :(-1//35*a*c^-1*(c+d*x^2)^-5//2*(-1d+c*a^2)^-1+1//7*x*c^-1*(c+d*x^2)^-7//2*arctan(a*x)+1//35*c^-4*(-1d+c*a^2)^-7//2*(-16*d^3+35*a^6*c^3+-70*d*a^4*c^2+56*c*a^2*d^2)*arctanh(a*(c+d*x^2)^(1/2)*(-1d+c*a^2)^-1//2)+6//35*x*c^-2*(c+d*x^2)^-5//2*arctan(a*x)+8//35*x*c^-3*(c+d*x^2)^-3//2*arctan(a*x)+16//35*x*c^-4*(c+d*x^2)^-1//2*arctan(a*x)+-1//35*a*c^-3*(c+d*x^2)^-1//2*(-1d+c*a^2)^-3*(8*d^2+19*a^4*c^2+-22*c*d*a^2)+-1//105*a*c^-2*(c+d*x^2)^-3//2*(-1d+c*a^2)^-2*(-6d+11*c*a^2))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+e*x^2), x) == :(-1//4*d*c^-4*(a+b*arctan(c*x))^2+1//4*d*x^4*(a+b*arctan(c*x))^2+1//6*e*c^-6*(a+b*arctan(c*x))^2+1//6*e*x^6*(a+b*arctan(c*x))^2+-4//45*e*b^2*c^-4*x^2+-1//3*d*b^2*c^-4*log(1+c^2*x^2)+1//12*d*b^2*c^-2*x^2+1//60*e*b^2*c^-2*x^4+23//90*e*b^2*c^-6*log(1+c^2*x^2)+(1/2)*a*b*d*x*c^-3+(1/2)*d*x*b^2*c^-3*arctan(c*x)+-1//3*a*b*e*x*c^-5+-1//3*e*x*b^2*c^-5*arctan(c*x)+-1//6*b*d*c^-1*x^3*(a+b*arctan(c*x))+-1//15*b*e*c^-1*x^5*(a+b*arctan(c*x))+1//9*b*e*c^-3*x^3*(a+b*arctan(c*x)))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+e*x^2), x) == :(1//3*d*x^3*(a+b*arctan(c*x))^2+1//5*e*x^5*(a+b*arctan(c*x))^2+-3//10*e*x*b^2*c^-4+-1//3*im*d*c^-3*(a+b*arctan(c*x))^2+-1//3*d*b^2*c^-3*arctan(c*x)+1//3*d*x*b^2*c^-2+1//5*im*e*c^-5*(a+b*arctan(c*x))^2+1//30*e*b^2*c^-2*x^3+3//10*e*b^2*c^-5*arctan(c*x)+-2//3*b*d*c^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//3*im*d*b^2*c^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//3*b*d*c^-1*x^2*(a+b*arctan(c*x))+-1//10*b*e*c^-1*x^4*(a+b*arctan(c*x))+1//5*im*e*b^2*c^-5*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+1//5*b*e*c^-3*x^2*(a+b*arctan(c*x))+2//5*b*e*c^-5*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x*(a+b*arctan(c*x))^2*(d+e*x^2), x) == :((1/2)*d*c^-2*(a+b*arctan(c*x))^2+(1/2)*d*x^2*(a+b*arctan(c*x))^2+-1//4*e*c^-4*(a+b*arctan(c*x))^2+1//4*e*x^4*(a+b*arctan(c*x))^2+(1/2)*d*b^2*c^-2*log(1+c^2*x^2)+-1//3*e*b^2*c^-4*log(1+c^2*x^2)+1//12*e*b^2*c^-2*x^2+(1/2)*a*b*e*x*c^-3+(1/2)*e*x*b^2*c^-3*arctan(c*x)+-1*a*b*d*x*c^-1+-1*d*x*b^2*c^-1*arctan(c*x)+-1//6*b*e*c^-1*x^3*(a+b*arctan(c*x)))
@test integrate((a+b*arctan(c*x))^2*(d+e*x^2), x) == :(d*x*(a+b*arctan(c*x))^2+1//3*e*x^3*(a+b*arctan(c*x))^2+im*d*c^-1*(a+b*arctan(c*x))^2+-1//3*im*e*c^-3*(a+b*arctan(c*x))^2+-1//3*e*b^2*c^-3*arctan(c*x)+1//3*e*x*b^2*c^-2+im*d*b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*b*d*c^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-2//3*b*e*c^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//3*im*e*b^2*c^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//3*b*e*c^-1*x^2*(a+b*arctan(c*x)))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+e*x^2), x) == :((1/2)*d*b^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+(1/2)*e*c^-2*(a+b*arctan(c*x))^2+(1/2)*e*x^2*(a+b*arctan(c*x))^2+2*d*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*d*b^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+(1/2)*e*b^2*c^-2*log(1+c^2*x^2)+im*b*d*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-1*im*b*d*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*a*b*e*x*c^-1+-1*e*x*b^2*c^-1*arctan(c*x))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+e*x^2), x) == :(e*x*(a+b*arctan(c*x))^2+-1*d*x^-1*(a+b*arctan(c*x))^2+im*e*c^-1*(a+b*arctan(c*x))^2+-1*im*c*d*(a+b*arctan(c*x))^2+im*e*b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*c*d*b^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+2*b*c*d*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+2*b*e*c^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+e*x^2), x) == :((1/2)*e*b^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+2*e*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*d*c^2*(a+b*arctan(c*x))^2+-1//2*d*x^-2*(a+b*arctan(c*x))^2+-1//2*e*b^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+d*b^2*c^2*log(x)+-1//2*d*b^2*c^2*log(1+c^2*x^2)+im*b*e*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-1*im*b*e*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*b*c*d*x^-1*(a+b*arctan(c*x)))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+e*x^2)^2, x) == :(-1//4*c^-4*d^2*(a+b*arctan(c*x))^2+-1//8*c^-8*e^2*(a+b*arctan(c*x))^2+1//4*d^2*x^4*(a+b*arctan(c*x))^2+1//8*e^2*x^8*(a+b*arctan(c*x))^2+-22//105*b^2*c^-8*e^2*log(1+c^2*x^2)+-3//140*b^2*c^-4*e^2*x^4+-1//3*b^2*c^-4*d^2*log(1+c^2*x^2)+1//3*d*e*c^-6*(a+b*arctan(c*x))^2+1//3*d*e*x^6*(a+b*arctan(c*x))^2+1//12*b^2*c^-2*d^2*x^2+1//168*b^2*c^-2*e^2*x^6+71//840*b^2*c^-6*e^2*x^2+(1/2)*a*b*x*c^-3*d^2+(1/2)*x*b^2*c^-3*d^2*arctan(c*x)+-8//45*d*e*b^2*c^-4*x^2+-1//6*b*c^-1*d^2*x^3*(a+b*arctan(c*x))+-1//12*b*c^-5*e^2*x^3*(a+b*arctan(c*x))+-1//28*b*c^-1*e^2*x^7*(a+b*arctan(c*x))+1//4*a*b*x*c^-7*e^2+1//4*x*b^2*c^-7*e^2*arctan(c*x)+1//20*b*c^-3*e^2*x^5*(a+b*arctan(c*x))+1//30*d*e*b^2*c^-2*x^4+23//45*d*e*b^2*c^-6*log(1+c^2*x^2)+-2//3*a*b*d*e*x*c^-5+-2//3*d*e*x*b^2*c^-5*arctan(c*x)+-2//15*b*d*e*c^-1*x^5*(a+b*arctan(c*x))+2//9*b*d*e*c^-3*x^3*(a+b*arctan(c*x)))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+e*x^2)^2, x) == :(1//3*d^2*x^3*(a+b*arctan(c*x))^2+1//7*e^2*x^7*(a+b*arctan(c*x))^2+-11//42*b^2*c^-7*e^2*arctan(c*x)+-5//126*b^2*c^-4*e^2*x^3+-1//3*im*c^-3*d^2*(a+b*arctan(c*x))^2+-1//3*b^2*c^-3*d^2*arctan(c*x)+-1//7*im*c^-7*e^2*(a+b*arctan(c*x))^2+1//3*x*b^2*c^-2*d^2+1//105*b^2*c^-2*e^2*x^5+2//5*d*e*x^5*(a+b*arctan(c*x))^2+11//42*x*b^2*c^-6*e^2+-3//5*d*e*x*b^2*c^-4+-2//3*b*c^-3*d^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-2//7*b*c^-7*e^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//3*im*b^2*c^-3*d^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//3*b*c^-1*d^2*x^2*(a+b*arctan(c*x))+-1//7*im*b^2*c^-7*e^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//7*b*c^-5*e^2*x^2*(a+b*arctan(c*x))+-1//21*b*c^-1*e^2*x^6*(a+b*arctan(c*x))+1//14*b*c^-3*e^2*x^4*(a+b*arctan(c*x))+1//15*d*e*b^2*c^-2*x^3+2//5*im*d*e*c^-5*(a+b*arctan(c*x))^2+3//5*d*e*b^2*c^-5*arctan(c*x)+-1//5*b*d*e*c^-1*x^4*(a+b*arctan(c*x))+2//5*im*d*e*b^2*c^-5*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2//5*b*d*e*c^-3*x^2*(a+b*arctan(c*x))+4//5*b*d*e*c^-5*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x*(a+b*arctan(c*x))^2*(d+e*x^2)^2, x) == :((1/2)*c^-2*d^2*(a+b*arctan(c*x))^2+(1/2)*d^2*x^2*(a+b*arctan(c*x))^2+1//6*c^-6*e^2*(a+b*arctan(c*x))^2+1//6*e^2*x^6*(a+b*arctan(c*x))^2+(1/2)*d*e*x^4*(a+b*arctan(c*x))^2+(1/2)*b^2*c^-2*d^2*log(1+c^2*x^2)+-4//45*b^2*c^-4*e^2*x^2+-1//2*d*e*c^-4*(a+b*arctan(c*x))^2+1//60*b^2*c^-2*e^2*x^4+23//90*b^2*c^-6*e^2*log(1+c^2*x^2)+-1*a*b*x*c^-1*d^2+-1*x*b^2*c^-1*d^2*arctan(c*x)+-2//3*d*e*b^2*c^-4*log(1+c^2*x^2)+-1//3*a*b*x*c^-5*e^2+-1//3*x*b^2*c^-5*e^2*arctan(c*x)+-1//15*b*c^-1*e^2*x^5*(a+b*arctan(c*x))+1//6*d*e*b^2*c^-2*x^2+1//9*b*c^-3*e^2*x^3*(a+b*arctan(c*x))+a*b*d*e*x*c^-3+d*e*x*b^2*c^-3*arctan(c*x)+-1//3*b*d*e*c^-1*x^3*(a+b*arctan(c*x)))
@test integrate((a+b*arctan(c*x))^2*(d+e*x^2)^2, x) == :(x*d^2*(a+b*arctan(c*x))^2+1//5*e^2*x^5*(a+b*arctan(c*x))^2+im*c^-1*d^2*(a+b*arctan(c*x))^2+-3//10*x*b^2*c^-4*e^2+1//5*im*c^-5*e^2*(a+b*arctan(c*x))^2+1//30*b^2*c^-2*e^2*x^3+2//3*d*e*x^3*(a+b*arctan(c*x))^2+3//10*b^2*c^-5*e^2*arctan(c*x)+im*b^2*c^-1*d^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*b*c^-1*d^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-2//3*im*d*e*c^-3*(a+b*arctan(c*x))^2+-2//3*d*e*b^2*c^-3*arctan(c*x)+-1//10*b*c^-1*e^2*x^4*(a+b*arctan(c*x))+1//5*im*b^2*c^-5*e^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+1//5*b*c^-3*e^2*x^2*(a+b*arctan(c*x))+2//3*d*e*x*b^2*c^-2+2//5*b*c^-5*e^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-4//3*b*d*e*c^-3*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-2//3*im*d*e*b^2*c^-3*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-2//3*b*d*e*c^-1*x^2*(a+b*arctan(c*x)))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+e*x^2)^2, x) == :((1/2)*b^2*d^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+2*d^2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*b^2*d^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//4*c^-4*e^2*(a+b*arctan(c*x))^2+1//4*e^2*x^4*(a+b*arctan(c*x))^2+d*e*c^-2*(a+b*arctan(c*x))^2+d*e*x^2*(a+b*arctan(c*x))^2+-1//3*b^2*c^-4*e^2*log(1+c^2*x^2)+1//12*b^2*c^-2*e^2*x^2+im*b*d^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+d*e*b^2*c^-2*log(1+c^2*x^2)+(1/2)*a*b*x*c^-3*e^2+(1/2)*x*b^2*c^-3*e^2*arctan(c*x)+-1*im*b*d^2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//6*b*c^-1*e^2*x^3*(a+b*arctan(c*x))+-2*a*b*d*e*x*c^-1+-2*d*e*x*b^2*c^-1*arctan(c*x))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+e*x^2)^2, x) == :(-1*d^2*x^-1*(a+b*arctan(c*x))^2+1//3*e^2*x^3*(a+b*arctan(c*x))^2+-1*im*c*d^2*(a+b*arctan(c*x))^2+2*d*e*x*(a+b*arctan(c*x))^2+-1//3*im*c^-3*e^2*(a+b*arctan(c*x))^2+-1//3*b^2*c^-3*e^2*arctan(c*x)+1//3*x*b^2*c^-2*e^2+-1*im*c*b^2*d^2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+2*im*d*e*c^-1*(a+b*arctan(c*x))^2+2*b*c*d^2*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-2//3*b*c^-3*e^2*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//3*im*b^2*c^-3*e^2*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//3*b*c^-1*e^2*x^2*(a+b*arctan(c*x))+2*im*d*e*b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+4*b*d*e*c^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+e*x^2)^2, x) == :((1/2)*c^-2*e^2*(a+b*arctan(c*x))^2+(1/2)*e^2*x^2*(a+b*arctan(c*x))^2+-1//2*c^2*d^2*(a+b*arctan(c*x))^2+-1//2*d^2*x^-2*(a+b*arctan(c*x))^2+d*e*b^2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+b^2*c^2*d^2*log(x)+(1/2)*b^2*c^-2*e^2*log(1+c^2*x^2)+-1*d*e*b^2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+4*d*e*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*b^2*c^2*d^2*log(1+c^2*x^2)+-1*a*b*x*c^-1*e^2+-1*b*c*d^2*x^-1*(a+b*arctan(c*x))+-1*x*b^2*c^-1*e^2*arctan(c*x)+-2*im*b*d*e*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*im*b*d*e*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+e*x^2)^-1, x) == :((1/2)*c^-2*e^-1*(a+b*arctan(c*x))^2+(1/2)*e^-1*x^2*(a+b*arctan(c*x))^2+d*e^-2*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+(1/2)*d*b^2*e^-2*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b^2*c^-2*e^-1*log(1+c^2*x^2)+-1//2*d*e^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*d*e^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//4*d*b^2*e^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*d*b^2*e^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*a*b*x*c^-1*e^-1+-1*x*b^2*c^-1*e^-1*arctan(c*x)+(1/2)*im*b*d*e^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*im*b*d*e^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*im*b*d*e^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+e*x^2)^-1, x) == :(x*e^-1*(a+b*arctan(c*x))^2+im*c^-1*e^-1*(a+b*arctan(c*x))^2+(1/2)*e^-3//2*(-1d)^(1/2)*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//2*e^-3//2*(-1d)^(1/2)*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*b^2*e^-3//2*(-1d)^(1/2)*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*b^2*e^-3//2*(-1d)^(1/2)*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+im*b^2*c^-1*e^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*b*c^-1*e^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+(1/2)*im*b*e^-3//2*(-1d)^(1/2)*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*im*b*e^-3//2*(-1d)^(1/2)*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x*(a+b*arctan(c*x))^2*(d+e*x^2)^-1, x) == :((1/2)*e^-1*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*e^-1*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*e^-1*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-1//2*b^2*e^-1*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+1//4*b^2*e^-1*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*b^2*e^-1*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+im*b*e^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//2*im*b*e^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*im*b*e^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate((a+b*arctan(c*x))^2*(d+e*x^2)^-1, x) == :((1/2)*e^-1//2*(-1d)^-1//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//2*e^-1//2*(-1d)^-1//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*b^2*e^-1//2*(-1d)^-1//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*b^2*e^-1//2*(-1d)^-1//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+(1/2)*im*b*e^-1//2*(-1d)^-1//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*im*b*e^-1//2*(-1d)^-1//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+e*x^2)^-1, x) == :(d^-1*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+(1/2)*b^2*d^-1*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+2*d^-1*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*b^2*d^-1*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//2*d^-1*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*d^-1*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//4*b^2*d^-1*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*b^2*d^-1*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+(1/2)*im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*b*d^-1*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+e*x^2)^-1, x) == :(-1*d^-1*x^-1*(a+b*arctan(c*x))^2+(1/2)*e^(1/2)*(-1d)^-3//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*im*c*d^-1*(a+b*arctan(c*x))^2+-1//2*e^(1/2)*(-1d)^-3//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*b^2*e^(1/2)*(-1d)^-3//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*b^2*e^(1/2)*(-1d)^-3//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*im*c*b^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+2*b*c*d^-1*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+(1/2)*im*b*e^(1/2)*(-1d)^-3//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*im*b*e^(1/2)*(-1d)^-3//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+e*x^2)^-1, x) == :(-1//2*c^2*d^-1*(a+b*arctan(c*x))^2+-1//2*d^-1*x^-2*(a+b*arctan(c*x))^2+b^2*c^2*d^-1*log(x)+(1/2)*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+(1/2)*e*d^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*e*d^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*e*d^-2*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-2*e*d^-2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+-1//2*e*b^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-1//2*b^2*c^2*d^-1*log(1+c^2*x^2)+1//4*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*b*c*d^-1*x^-1*(a+b*arctan(c*x))+im*b*e*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+im*b*e*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1*im*b*e*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+-1//2*im*b*e*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*im*b*e*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^3*(a+b*arctan(c*x))^2*(d+e*x^2)^-2, x) == :((1/2)*e^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*e^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*e^-2*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-1//2*b^2*e^-2*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+1//4*b^2*e^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*b^2*e^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+1//4*e^-2*(1+x*e^(1/2)*(-1d)^-1//2)^-1*(a+b*arctan(c*x))^2+1//4*e^-2*(1+-1*x*e^(1/2)*(-1d)^-1//2)^-1*(a+b*arctan(c*x))^2+im*b*e^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1*d*c^2*e^-2*(a+b*arctan(c*x))^2*(-2*e+2*d*c^2)^-1+-1//2*im*b*e^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*im*b*e^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+im*c*b^2*e^-3//2*(-1d)^(1/2)*(-4*e+4*d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+b*c*e^-3//2*(-1d)^(1/2)*(-2*e+2*d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1*im*c*b^2*e^-3//2*(-1d)^(1/2)*(-4*e+4*d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1*b*c*e^-3//2*(-1d)^(1/2)*(-2*e+2*d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^2*(a+b*arctan(c*x))^2*(d+e*x^2)^-2, x) == :(-1//4*e^-3//2*(a+b*arctan(c*x))^2*((-1d)^(1/2)+x*e^(1/2))^-1+1//4*e^-3//2*(a+b*arctan(c*x))^2*((-1d)^(1/2)+-1*x*e^(1/2))^-1+-1//4*e^-3//2*(-1d)^-1//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//8*b^2*e^-3//2*(-1d)^-1//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*e^-3//2*(-1d)^-1//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+1//8*b^2*e^-3//2*(-1d)^-1//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*im*c*e^-1*(a+b*arctan(c*x))^2*(-2*e+2*d*c^2)^-1+im*c*b^2*e^-1*(-4*e+4*d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+im*c*b^2*e^-1*(-4*e+4*d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+b*c*e^-1*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1*im*c*b^2*e^-1*(-2*e+2*d*c^2)^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*c*b^2*e^-1*(-2*e+2*d*c^2)^-1*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1*b*c*e^-1*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1*b*c*e^-1*(-2*e+2*d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1*b*c*e^-1*(-2*e+2*d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//4*im*b*e^-3//2*(-1d)^-1//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+1//4*im*b*e^-3//2*(-1d)^-1//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2))))
@test integrate(x*(a+b*arctan(c*x))^2*(d+e*x^2)^-2, x) == :(c^2*e^-1*(a+b*arctan(c*x))^2*(-2*e+2*d*c^2)^-1+-1//4*d^-1*e^-1*(1+x*e^(1/2)*(-1d)^-1//2)^-1*(a+b*arctan(c*x))^2+-1//4*d^-1*e^-1*(1+-1*x*e^(1/2)*(-1d)^-1//2)^-1*(a+b*arctan(c*x))^2+(1/2)*b*c*e^-1//2*(-1d)^-1//2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*b*c*e^-1//2*(-1d)^-1//2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//4*im*c*b^2*e^-1//2*(-1d)^-1//2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*im*c*b^2*e^-1//2*(-1d)^-1//2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate((a+b*arctan(c*x))^2*(d+e*x^2)^-2, x) == :(-1//4*d^-1*e^-1//2*(a+b*arctan(c*x))^2*((-1d)^(1/2)+-1*x*e^(1/2))^-1+-1//4*e^-1//2*(-1d)^-3//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//8*b^2*e^-1//2*(-1d)^-3//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+1//4*d^-1*e^-1//2*(a+b*arctan(c*x))^2*((-1d)^(1/2)+x*e^(1/2))^-1+1//4*e^-1//2*(-1d)^-3//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//8*b^2*e^-1//2*(-1d)^-3//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*im*c*d^-1*(a+b*arctan(c*x))^2*(-1*e+d*c^2)^-1+b*c*d^-1*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+(1/2)*im*c*b^2*d^-1*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+(1/2)*im*c*b^2*d^-1*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b*c*d^-1*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*b*c*d^-1*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*b*c*d^-1*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1//4*im*b*e^-1//2*(-1d)^-3//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*im*c*b^2*d^-1*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*im*c*b^2*d^-1*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+1//4*im*b*e^-1//2*(-1d)^-3//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^-1*(a+b*arctan(c*x))^2*(d+e*x^2)^-2, x) == :(d^-2*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+(1/2)*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+2*d^-2*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-1//2*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+-1//2*d^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*d^-2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//4*b^2*d^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//4*b^2*d^-2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+1//4*d^-2*(1+x*e^(1/2)*(-1d)^-1//2)^-1*(a+b*arctan(c*x))^2+1//4*d^-2*(1+-1*x*e^(1/2)*(-1d)^-1//2)^-1*(a+b*arctan(c*x))^2+-1//2*c^2*d^-1*(a+b*arctan(c*x))^2*(-1*e+d*c^2)^-1+im*b*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+(1/2)*im*b*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*im*b*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*im*b*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1*im*b*d^-2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b*c*e^(1/2)*(-1d)^-3//2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*b*c*e^(1/2)*(-1d)^-3//2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//4*im*c*b^2*e^(1/2)*(-1d)^-3//2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*im*c*b^2*e^(1/2)*(-1d)^-3//2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^-2*(a+b*arctan(c*x))^2*(d+e*x^2)^-2, x) == :(-1*d^-2*x^-1*(a+b*arctan(c*x))^2+-1*im*c*d^-2*(a+b*arctan(c*x))^2+-3//4*e^(1/2)*(-1d)^-5//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-3//8*b^2*e^(1/2)*(-1d)^-5//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//4*d^-2*e^(1/2)*(a+b*arctan(c*x))^2*((-1d)^(1/2)+x*e^(1/2))^-1+1//4*d^-2*e^(1/2)*(a+b*arctan(c*x))^2*((-1d)^(1/2)+-1*x*e^(1/2))^-1+3//4*e^(1/2)*(-1d)^-5//2*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+3//8*b^2*e^(1/2)*(-1d)^-5//2*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1*im*c*b^2*d^-2*Polylogarithms.polylog(2,-1+2*(1+-1*im*c*x)^-1)+2*b*c*d^-2*(a+b*arctan(c*x))*log(2+-2*(1+-1*im*c*x)^-1)+-3//4*im*b*e^(1/2)*(-1d)^-5//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*im*c*e*d^-2*(a+b*arctan(c*x))^2*(-1*e+d*c^2)^-1+3//4*im*b*e^(1/2)*(-1d)^-5//2*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+b*c*e*d^-2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*(1+-1*im*c*x)^-1)+-1*b*c*e*d^-2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*(1+im*c*x)^-1)+-1//2*im*c*e*b^2*d^-2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+-1//2*im*c*e*b^2*d^-2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+-1//2*b*c*e*d^-2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*b*c*e*d^-2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+1//4*im*c*e*b^2*d^-2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*im*c*e*b^2*d^-2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^-3*(a+b*arctan(c*x))^2*(d+e*x^2)^-2, x) == :(-1//2*c^2*d^-2*(a+b*arctan(c*x))^2+-1//2*d^-2*x^-2*(a+b*arctan(c*x))^2+e*b^2*d^-3*Polylogarithms.polylog(3,1+-2*(1+im*c*x)^-1)+e*d^-3*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+e*d^-3*(a+b*arctan(c*x))^2*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+b^2*c^2*d^-2*log(x)+(1/2)*e*b^2*d^-3*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+(1/2)*e*b^2*d^-3*Polylogarithms.polylog(3,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1*e*b^2*d^-3*Polylogarithms.polylog(3,1+-2*(1+-1*im*c*x)^-1)+-1*e*b^2*d^-3*Polylogarithms.polylog(3,-1+2*(1+im*c*x)^-1)+-4*e*d^-3*(a+b*arctan(c*x))^2*arctanh(1+-2*(1+im*c*x)^-1)+-2*e*d^-3*(a+b*arctan(c*x))^2*log(2*(1+-1*im*c*x)^-1)+-1//2*b^2*c^2*d^-2*log(1+c^2*x^2)+-1//4*e*d^-3*(1+x*e^(1/2)*(-1d)^-1//2)^-1*(a+b*arctan(c*x))^2+-1//4*e*d^-3*(1+-1*x*e^(1/2)*(-1d)^-1//2)^-1*(a+b*arctan(c*x))^2+(1/2)*e*c^2*d^-2*(a+b*arctan(c*x))^2*(-1*e+d*c^2)^-1+-1*b*c*d^-2*x^-1*(a+b*arctan(c*x))+-1*im*b*e*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1*im*b*e*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-2*im*b*e*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,-1+2*(1+im*c*x)^-1)+2*im*b*e*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+im*c*x)^-1)+2*im*b*e*d^-3*(a+b*arctan(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b*c*e^3//2*(-1d)^-5//2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+-1//2*b*c*e^3//2*(-1d)^-5//2*(-1*e+d*c^2)^-1*(a+b*arctan(c*x))*log(2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2)))+-1//4*im*c*b^2*e^3//2*(-1d)^-5//2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*e^(1/2)+c*(-1d)^(1/2))^-1*((-1d)^(1/2)+x*e^(1/2)))+1//4*im*c*b^2*e^3//2*(-1d)^-5//2*(-1*e+d*c^2)^-1*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1d)^(1/2)+-1*im*e^(1/2))^-1*((-1d)^(1/2)+-1*x*e^(1/2))))
@test integrate(x^4*arctan(x)*log(1+x^2), x) == :(-77//300*x^2+-1//20*log(1+x^2)^2+1//5*arctan(x)^2+9//200*x^4+137//300*log(1+x^2)+-2//5*x*arctan(x)+-2//25*x^5*arctan(x)+-1//20*x^4*log(1+x^2)+1//10*x^2*log(1+x^2)+2//15*x^3*arctan(x)+1//5*x^5*arctan(x)*log(1+x^2))
@test integrate(x^3*arctan(x)*log(1+x^2), x) == :(-25//24*x+7//72*x^3+25//24*arctan(x)+-1//4*arctan(x)*log(1+x^2)+-1//8*x^4*arctan(x)+-1//12*x^3*log(1+x^2)+1//4*x*log(1+x^2)+1//4*x^2*arctan(x)+1//4*x^4*arctan(x)*log(1+x^2))
@test integrate(x^2*arctan(x)*log(1+x^2), x) == :(-11//18*log(1+x^2)+-1//3*arctan(x)^2+1//12*log(1+x^2)^2+5//18*x^2+-2//9*x^3*arctan(x)+-1//6*x^2*log(1+x^2)+2//3*x*arctan(x)+1//3*x^3*arctan(x)*log(1+x^2))
@test integrate(x*arctan(x)*log(1+x^2), x) == :(-3//2*arctan(x)+3//2*x+-1//2*x*log(1+x^2)+-1//2*x^2*arctan(x)+(1/2+(1/2)*x^2)*arctan(x)*log(1+x^2))
@test integrate(arctan(x)*log(1+x^2), x) == :(arctan(x)^2+-1//4*log(1+x^2)^2+-2*x*arctan(x)+x*arctan(x)*log(1+x^2)+log(1+x^2))
@test integrate(x^-1*arctan(x)*log(1+x^2), x) == :(im*Polylogarithms.polylog(3,1+im*x)+-1*im*Polylogarithms.polylog(3,1+-1*im*x)+im*Polylogarithms.polylog(2,1+-1*im*x)*log(1+-1*im*x)+(1/2)*im*log(1+-1*im*x)^2*log(im*x)+(1/2)*im*(-1*log(1+x^2)+log(1+im*x)+log(1+-1*im*x))*Polylogarithms.polylog(2,im*x)+-1*im*Polylogarithms.polylog(2,1+im*x)*log(1+im*x)+-1//2*im*log(1+im*x)^2*log(-1*im*x)+-1//2*im*(-1*log(1+x^2)+log(1+im*x)+log(1+-1*im*x))*Polylogarithms.polylog(2,-1*im*x))
@test integrate(x^-2*arctan(x)*log(1+x^2), x) == :(arctan(x)^2+-1//2*Polylogarithms.polylog(2,-1*x^2)+-1//4*log(1+x^2)^2+-1*x^-1*arctan(x)*log(1+x^2))
@test integrate(x^-3*arctan(x)*log(1+x^2), x) == :((1/2)*im*Polylogarithms.polylog(2,-1*im*x)+-1//2*im*Polylogarithms.polylog(2,im*x)+-1//2*x^-1*log(1+x^2)+-1//2*arctan(x)*log(1+x^2)+-1//2*x^-2*arctan(x)*log(1+x^2)+arctan(x))
@test integrate(x^-4*arctan(x)*log(1+x^2), x) == :(-1//2*log(1+x^2)+-1//3*arctan(x)^2+1//6*Polylogarithms.polylog(2,-1*x^2)+1//12*log(1+x^2)^2+-2//3*x^-1*arctan(x)+-1//6*x^-2*log(1+x^2)+-1//3*x^-3*arctan(x)*log(1+x^2)+log(x))
@test integrate(x^-5*arctan(x)*log(1+x^2), x) == :(-11//12*arctan(x)+-5//12*x^-1+-1//4*im*Polylogarithms.polylog(2,-1*im*x)+-1//4*x^-2*arctan(x)+-1//12*x^-3*log(1+x^2)+1//4*im*Polylogarithms.polylog(2,im*x)+1//4*x^-1*log(1+x^2)+1//4*arctan(x)*log(1+x^2)+-1//4*x^-4*arctan(x)*log(1+x^2))
@test integrate(x^-6*arctan(x)*log(1+x^2), x) == :(-7//60*x^-2+-5//6*log(x)+-1//10*Polylogarithms.polylog(2,-1*x^2)+-1//20*log(1+x^2)^2+1//5*arctan(x)^2+5//12*log(1+x^2)+-2//15*x^-3*arctan(x)+-1//20*x^-4*log(1+x^2)+1//10*x^-2*log(1+x^2)+2//5*x^-1*arctan(x)+-1//5*x^-5*arctan(x)*log(1+x^2))
@test integrate(x^4*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(-2//25*a*e*x^5+1//5*x^5*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2))+-77//300*b*e*c^-3*x^2+-2//5*a*e*x*c^-4+-2//25*b*e*x^5*arctan(c*x)+-1//10*b*c^-5*(d+e*log(1+c^2*x^2))*log(1+c^2*x^2)+-1//20*b*c^-1*x^4*(d+e*log(1+c^2*x^2))+1//5*b*e*c^-5*arctan(c*x)^2+1//10*b*c^-3*x^2*(d+e*log(1+c^2*x^2))+1//20*b*e*c^-5*log(1+c^2*x^2)^2+2//5*a*e*c^-5*arctan(c*x)+2//15*a*e*c^-2*x^3+9//200*b*e*c^-1*x^4+137//300*b*e*c^-5*log(1+c^2*x^2)+-2//5*b*e*x*c^-4*arctan(c*x)+2//15*b*e*c^-2*x^3*arctan(c*x))
@test integrate(x^3*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(-1//8*e*x^4*(a+b*arctan(c*x))+1//4*x^4*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2))+-2//3*b*e*x*c^-3+-1//4*e*c^-4*(a+b*arctan(c*x))*log(1+c^2*x^2)+-1//8*b*c^-4*(-3*e+2d)*arctan(c*x)+-1//24*b*c^-1*x^3*(-1*e+2d)+1//4*e*c^-2*x^2*(a+b*arctan(c*x))+1//8*b*x*c^-3*(-3*e+2d)+1//18*b*e*c^-1*x^3+2//3*b*e*c^-4*arctan(c*x)+-1//12*b*e*c^-1*x^3*log(1+c^2*x^2)+1//4*b*e*x*c^-3*log(1+c^2*x^2))
@test integrate(x^2*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(-2//9*a*e*x^3+1//3*x^3*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2))+-11//18*b*e*c^-3*log(1+c^2*x^2)+-2//3*a*e*c^-3*arctan(c*x)+-2//9*b*e*x^3*arctan(c*x)+-1//3*b*e*c^-3*arctan(c*x)^2+-1//6*b*c^-1*x^2*(d+e*log(1+c^2*x^2))+-1//12*b*e*c^-3*log(1+c^2*x^2)^2+1//6*b*c^-3*(d+e*log(1+c^2*x^2))*log(1+c^2*x^2)+2//3*a*e*x*c^-2+5//18*b*e*c^-1*x^2+2//3*b*e*x*c^-2*arctan(c*x))
@test integrate(x*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :((1/2)*d*x^2*(a+b*arctan(c*x))+-1//2*e*x^2*(a+b*arctan(c*x))+b*e*x*c^-1+(1/2)*b*c^-2*(d+-1*e)*arctan(c*x)+-1*b*e*c^-2*arctan(c*x)+-1//2*b*x*c^-1*(d+-1*e)+(1/2)*e*c^-2*(1+c^2*x^2)*(a+b*arctan(c*x))*log(1+c^2*x^2)+-1//2*b*e*x*c^-1*log(1+c^2*x^2))
@test integrate((a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(x*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2))+-2*a*e*x+b*e*c^-1*log(1+c^2*x^2)+e*b^-1*c^-1*(a+b*arctan(c*x))^2+-2*b*e*x*arctan(c*x)+-1//4*b*c^-1*e^-1*(d+e*log(1+c^2*x^2))^2)
@test integrate(x^-1*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(a*d*log(x)+-1//2*a*e*Polylogarithms.polylog(2,-1*c^2*x^2)+im*b*e*Polylogarithms.polylog(3,1+im*c*x)+(1/2)*im*b*d*Polylogarithms.polylog(2,-1*im*c*x)+-1*im*b*e*Polylogarithms.polylog(3,1+-1*im*c*x)+-1//2*im*b*d*Polylogarithms.polylog(2,im*c*x)+im*b*e*Polylogarithms.polylog(2,1+-1*im*c*x)*log(1+-1*im*c*x)+(1/2)*im*b*e*log(1+-1*im*c*x)^2*log(im*c*x)+(1/2)*im*b*e*(-1*log(1+c^2*x^2)+log(1+im*c*x)+log(1+-1*im*c*x))*Polylogarithms.polylog(2,im*c*x)+-1*im*b*e*Polylogarithms.polylog(2,1+im*c*x)*log(1+im*c*x)+-1//2*im*b*e*log(1+im*c*x)^2*log(-1*im*c*x)+-1//2*im*b*e*(-1*log(1+c^2*x^2)+log(1+im*c*x)+log(1+-1*im*c*x))*Polylogarithms.polylog(2,-1*im*c*x))
@test integrate(x^-2*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(-1*x^-1*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2))+c*e*b^-1*(a+b*arctan(c*x))^2+(1/2)*b*c*(d+e*log(1+c^2*x^2))*log(1+-1*(1+c^2*x^2)^-1)+-1//2*b*c*e*Polylogarithms.polylog(2,(1+c^2*x^2)^-1))
@test integrate(x^-3*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(-1//2*x^-2*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2))+a*e*c^2*log(x)+b*e*c^2*arctan(c*x)+-1//2*a*e*c^2*log(1+c^2*x^2)+-1//2*b*c*x^-1*(d+e*log(1+c^2*x^2))+-1//2*b*c^2*(d+e*log(1+c^2*x^2))*arctan(c*x)+(1/2)*im*b*e*c^2*Polylogarithms.polylog(2,-1*im*c*x)+-1//2*im*b*e*c^2*Polylogarithms.polylog(2,im*c*x))
@test integrate(x^-4*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(-1//3*x^-3*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2))+b*e*c^3*log(x)+-2//3*e*c^2*x^-1*(a+b*arctan(c*x))+-1//3*b*e*c^3*log(1+c^2*x^2)+-1//3*e*b^-1*c^3*(a+b*arctan(c*x))^2+-1//6*b*c^3*(d+e*log(1+c^2*x^2))*log(1+-1*(1+c^2*x^2)^-1)+1//6*b*e*c^3*Polylogarithms.polylog(2,(1+c^2*x^2)^-1)+-1//6*b*c*x^-2*(1+c^2*x^2)*(d+e*log(1+c^2*x^2)))
@test integrate(x^-5*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(-1//4*x^-4*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2))+-11//12*b*e*c^4*arctan(c*x)+-5//12*b*e*c^3*x^-1+-1//2*a*e*c^4*log(x)+-1//4*a*e*c^2*x^-2+-1//12*b*c*x^-3*(d+e*log(1+c^2*x^2))+1//4*a*e*c^4*log(1+c^2*x^2)+1//4*b*c^3*x^-1*(d+e*log(1+c^2*x^2))+1//4*b*c^4*(d+e*log(1+c^2*x^2))*arctan(c*x)+-1//4*im*b*e*c^4*Polylogarithms.polylog(2,-1*im*c*x)+-1//4*b*e*c^2*x^-2*arctan(c*x)+1//4*im*b*e*c^4*Polylogarithms.polylog(2,im*c*x))
@test integrate(x^-6*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2)), x) == :(-1//5*x^-5*(a+b*arctan(c*x))*(d+e*log(1+c^2*x^2))+-7//60*b*e*c^3*x^-2+-5//6*b*e*c^5*log(x)+-2//15*e*c^2*x^-3*(a+b*arctan(c*x))+-1//10*b*e*c^5*Polylogarithms.polylog(2,(1+c^2*x^2)^-1)+-1//20*b*c*x^-4*(d+e*log(1+c^2*x^2))+1//5*e*b^-1*c^5*(a+b*arctan(c*x))^2+1//10*b*c^5*(d+e*log(1+c^2*x^2))*log(1+-1*(1+c^2*x^2)^-1)+2//5*e*c^4*x^-1*(a+b*arctan(c*x))+19//60*b*e*c^5*log(1+c^2*x^2)+1//10*b*c^3*x^-2*(1+c^2*x^2)*(d+e*log(1+c^2*x^2)))
@test integrate(x*(a+b*arctan(c*x))*(d+e*log(f+g*x^2)), x) == :((1/2)*d*x^2*(a+b*arctan(c*x))+-1//2*e*x^2*(a+b*arctan(c*x))+b*e*x*c^-1+(1/2)*b*c^-2*(d+-1*e)*arctan(c*x)+-1//2*b*x*c^-1*(d+-1*e)+(1/2)*e*g^-1*(a+b*arctan(c*x))*(f+g*x^2)*log(f+g*x^2)+-1//2*b*e*x*c^-1*log(f+g*x^2)+-1*b*e*c^-1*f^(1/2)*g^-1//2*arctan(x*f^-1//2*g^(1/2))+(1/2)*im*b*e*c^-2*g^-1*(-1g+f*c^2)*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b*e*c^-2*g^-1*(-1g+f*c^2)*arctan(c*x)*log(2*c*(1+-1*im*c*x)^-1*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))+(1/2)*b*e*c^-2*g^-1*(-1g+f*c^2)*arctan(c*x)*log(2*c*(1+-1*im*c*x)^-1*(c*(-1*f)^(1/2)+-1*im*g^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))+-1*b*e*c^-2*g^-1*(-1g+f*c^2)*arctan(c*x)*log(2*(1+-1*im*c*x)^-1)+-1//2*b*e*c^-2*g^-1*(-1g+f*c^2)*arctan(c*x)*log(f+g*x^2)+-1//4*im*b*e*c^-2*g^-1*(-1g+f*c^2)*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))+-1//4*im*b*e*c^-2*g^-1*(-1g+f*c^2)*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1*f)^(1/2)+-1*im*g^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2))))
@test integrate((a+b*arctan(c*x))*(d+e*log(f+g*x^2)), x) == :(x*(a+b*arctan(c*x))*(d+e*log(f+g*x^2))+-2*a*e*x+b*e*c^-1*log(1+c^2*x^2)+-2*b*e*x*arctan(c*x)+-1//2*b*e*c^-1*Polylogarithms.polylog(2,c^2*(-1g+f*c^2)^-1*(f+g*x^2))+-1//2*b*c^-1*(d+e*log(f+g*x^2))*log(-1*g*(-1g+f*c^2)^-1*(1+c^2*x^2))+2*a*e*f^(1/2)*g^-1//2*arctan(x*f^-1//2*g^(1/2))+(1/2)*im*b*e*g^-1//2*(-1*f)^(1/2)*Polylogarithms.polylog(2,g^(1/2)*(g^(1/2)+im*c*(-1*f)^(1/2))^-1*(1+im*c*x))+(1/2)*im*b*e*g^-1//2*(-1*f)^(1/2)*Polylogarithms.polylog(2,g^(1/2)*(g^(1/2)+im*c*(-1*f)^(1/2))^-1*(1+-1*im*c*x))+-1//2*im*b*e*g^-1//2*(-1*f)^(1/2)*Polylogarithms.polylog(2,g^(1/2)*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*(im+c*x))+-1//2*im*b*e*g^-1//2*(-1*f)^(1/2)*Polylogarithms.polylog(2,g^(1/2)*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*(im+-1*c*x))+(1/2)*im*b*e*g^-1//2*(-1*f)^(1/2)*log(c*(c*(-1*f)^(1/2)+-1*im*g^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))*log(1+-1*im*c*x)+(1/2)*im*b*e*g^-1//2*(-1*f)^(1/2)*log(c*(c*(-1*f)^(1/2)+-1*im*g^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))*log(1+im*c*x)+-1//2*im*b*e*g^-1//2*(-1*f)^(1/2)*log(c*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))*log(1+im*c*x)+-1//2*im*b*e*g^-1//2*(-1*f)^(1/2)*log(c*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))*log(1+-1*im*c*x))
@test integrate(x^-2*(a+b*arctan(c*x))*(d+e*log(f+g*x^2)), x) == :(-1*x^-1*(a+b*arctan(c*x))*(d+e*log(f+g*x^2))+(1/2)*b*c*e*Polylogarithms.polylog(2,1+g*f^-1*x^2)+(1/2)*b*c*(d+e*log(f+g*x^2))*log(-1*g*f^-1*x^2)+-1//2*b*c*e*Polylogarithms.polylog(2,c^2*(-1g+f*c^2)^-1*(f+g*x^2))+-1//2*b*c*(d+e*log(f+g*x^2))*log(-1*g*(-1g+f*c^2)^-1*(1+c^2*x^2))+2*a*e*f^-1//2*g^(1/2)*arctan(x*f^-1//2*g^(1/2))+(1/2)*im*b*e*g^(1/2)*(-1*f)^-1//2*Polylogarithms.polylog(2,g^(1/2)*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*(im+c*x))+(1/2)*im*b*e*g^(1/2)*(-1*f)^-1//2*Polylogarithms.polylog(2,g^(1/2)*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*(im+-1*c*x))+-1//2*im*b*e*g^(1/2)*(-1*f)^-1//2*Polylogarithms.polylog(2,g^(1/2)*(g^(1/2)+im*c*(-1*f)^(1/2))^-1*(1+im*c*x))+-1//2*im*b*e*g^(1/2)*(-1*f)^-1//2*Polylogarithms.polylog(2,g^(1/2)*(g^(1/2)+im*c*(-1*f)^(1/2))^-1*(1+-1*im*c*x))+(1/2)*im*b*e*g^(1/2)*(-1*f)^-1//2*log(c*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))*log(1+im*c*x)+(1/2)*im*b*e*g^(1/2)*(-1*f)^-1//2*log(c*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))*log(1+-1*im*c*x)+-1//2*im*b*e*g^(1/2)*(-1*f)^-1//2*log(c*(c*(-1*f)^(1/2)+-1*im*g^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))*log(1+-1*im*c*x)+-1//2*im*b*e*g^(1/2)*(-1*f)^-1//2*log(c*(c*(-1*f)^(1/2)+-1*im*g^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))*log(1+im*c*x))
@test integrate(x^-3*(a+b*arctan(c*x))*(d+e*log(f+g*x^2)), x) == :(-1//2*x^-2*(a+b*arctan(c*x))*(d+e*log(f+g*x^2))+-1//2*b*c*x^-1*(d+e*log(f+g*x^2))+-1//2*b*c^2*(d+e*log(f+g*x^2))*arctan(c*x)+a*e*g*f^-1*log(x)+-1//2*a*e*g*f^-1*log(f+g*x^2)+b*c*e*f^-1//2*g^(1/2)*arctan(x*f^-1//2*g^(1/2))+(1/2)*im*b*e*g*f^-1*Polylogarithms.polylog(2,-1*im*c*x)+(1/2)*im*b*e*f^-1*(-1g+f*c^2)*Polylogarithms.polylog(2,1+-2*(1+-1*im*c*x)^-1)+(1/2)*b*e*f^-1*(-1g+f*c^2)*arctan(c*x)*log(2*c*(1+-1*im*c*x)^-1*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))+(1/2)*b*e*f^-1*(-1g+f*c^2)*arctan(c*x)*log(2*c*(1+-1*im*c*x)^-1*(c*(-1*f)^(1/2)+-1*im*g^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))+-1*b*e*f^-1*(-1g+f*c^2)*arctan(c*x)*log(2*(1+-1*im*c*x)^-1)+-1//2*im*b*e*g*f^-1*Polylogarithms.polylog(2,im*c*x)+-1//4*im*b*e*f^-1*(-1g+f*c^2)*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(im*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))+-1//4*im*b*e*f^-1*(-1g+f*c^2)*Polylogarithms.polylog(2,1+-2*c*(1+-1*im*c*x)^-1*(c*(-1*f)^(1/2)+-1*im*g^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2))))

max_stars_repo_path: test/5 Inverse trig functions/5.3 Inverse tangent/5.3.4 u (a+b arctan(c x))^p.jl