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

@test integrate(x^3*(a+b*arctanh(c*x))*(d+c*d*x), x) == :(1//4*d*x^4*(a+b*arctanh(c*x))+1//20*b*d*x^4+-1//40*b*d*c^-4*log(1+c*x)+1//4*b*d*x*c^-3+1//5*c*d*x^5*(a+b*arctanh(c*x))+1//10*b*d*c^-2*x^2+1//12*b*d*c^-1*x^3+9//40*b*d*c^-4*log(1+-1*c*x))
@test integrate(x^2*(a+b*arctanh(c*x))*(d+c*d*x), x) == :(1//3*d*x^3*(a+b*arctanh(c*x))+1//12*b*d*x^3+1//4*b*d*x*c^-2+1//4*c*d*x^4*(a+b*arctanh(c*x))+1//6*b*d*c^-1*x^2+1//24*b*d*c^-3*log(1+c*x)+7//24*b*d*c^-3*log(1+-1*c*x))
@test integrate(x*(a+b*arctanh(c*x))*(d+c*d*x), x) == :((1/2)*d*x^2*(a+b*arctanh(c*x))+1//6*b*d*x^2+(1/2)*b*d*x*c^-1+-1//12*b*d*c^-2*log(1+c*x)+1//3*c*d*x^3*(a+b*arctanh(c*x))+5//12*b*d*c^-2*log(1+-1*c*x))
@test integrate((a+b*arctanh(c*x))*(d+c*d*x), x) == :((1/2)*b*d*x+b*d*c^-1*log(1+-1*c*x)+(1/2)*d*c^-1*(1+c*x)^2*(a+b*arctanh(c*x)))
@test integrate(x^-1*(a+b*arctanh(c*x))*(d+c*d*x), x) == :(a*d*log(x)+(1/2)*b*d*Polylogarithms.polylog(2,c*x)+(1/2)*b*d*log(1+-1*c^2*x^2)+-1//2*b*d*Polylogarithms.polylog(2,-1*c*x)+a*c*d*x+b*c*d*x*arctanh(c*x))
@test integrate(x^-2*(a+b*arctanh(c*x))*(d+c*d*x), x) == :(-1*d*x^-1*(a+b*arctanh(c*x))+a*c*d*log(x)+b*c*d*log(x)+(1/2)*b*c*d*Polylogarithms.polylog(2,c*x)+-1//2*b*c*d*Polylogarithms.polylog(2,-1*c*x)+-1//2*b*c*d*log(1+-1*c^2*x^2))
@test integrate(x^-3*(a+b*arctanh(c*x))*(d+c*d*x), x) == :(b*d*c^2*log(x)+-1*b*d*c^2*log(1+-1*c*x)+-1//2*b*c*d*x^-1+-1//2*d*x^-2*(1+c*x)^2*(a+b*arctanh(c*x)))
@test integrate(x^-4*(a+b*arctanh(c*x))*(d+c*d*x), x) == :(-1//3*d*x^-3*(a+b*arctanh(c*x))+-5//12*b*d*c^3*log(1+-1*c*x)+-1//2*b*d*c^2*x^-1+-1//2*c*d*x^-2*(a+b*arctanh(c*x))+-1//6*b*c*d*x^-2+1//3*b*d*c^3*log(x)+1//12*b*d*c^3*log(1+c*x))
@test integrate(x^-5*(a+b*arctanh(c*x))*(d+c*d*x), x) == :(-1//4*d*x^-4*(a+b*arctanh(c*x))+-7//24*b*d*c^4*log(1+-1*c*x)+-1//3*c*d*x^-3*(a+b*arctanh(c*x))+-1//4*b*d*c^3*x^-1+-1//6*b*d*c^2*x^-2+-1//12*b*c*d*x^-3+-1//24*b*d*c^4*log(1+c*x)+1//3*b*d*c^4*log(x))
@test integrate(x^3*(d+c*d*x)^2*(a+b*arctanh(c*x)), x) == :(1//4*d^2*x^4*(a+b*arctanh(c*x))+1//10*b*d^2*x^4+-1//120*b*c^-4*d^2*log(1+c*x)+1//5*b*c^-2*d^2*x^2+1//6*c^2*d^2*x^6*(a+b*arctanh(c*x))+1//30*b*c*d^2*x^5+2//5*c*d^2*x^5*(a+b*arctanh(c*x))+5//12*b*x*c^-3*d^2+5//36*b*c^-1*d^2*x^3+49//120*b*c^-4*d^2*log(1+-1*c*x))
@test integrate(x^2*(d+c*d*x)^2*(a+b*arctanh(c*x)), x) == :(1//3*d^2*x^3*(a+b*arctanh(c*x))+1//6*b*d^2*x^3+(1/2)*b*x*c^-2*d^2+(1/2)*c*d^2*x^4*(a+b*arctanh(c*x))+1//5*c^2*d^2*x^5*(a+b*arctanh(c*x))+1//20*b*c*d^2*x^4+1//60*b*c^-3*d^2*log(1+c*x)+4//15*b*c^-1*d^2*x^2+31//60*b*c^-3*d^2*log(1+-1*c*x))
@test integrate(x*(d+c*d*x)^2*(a+b*arctanh(c*x)), x) == :((1/2)*d^2*x^2*(a+b*arctanh(c*x))+1//3*b*d^2*x^2+-1//24*b*c^-2*d^2*log(1+c*x)+1//4*c^2*d^2*x^4*(a+b*arctanh(c*x))+1//12*b*c*d^2*x^3+2//3*c*d^2*x^3*(a+b*arctanh(c*x))+3//4*b*x*c^-1*d^2+17//24*b*c^-2*d^2*log(1+-1*c*x))
@test integrate((d+c*d*x)^2*(a+b*arctanh(c*x)), x) == :(2//3*b*x*d^2+1//3*c^-1*d^2*(1+c*x)^3*(a+b*arctanh(c*x))+1//6*b*c^-1*d^2*(1+c*x)^2+4//3*b*c^-1*d^2*log(1+-1*c*x))
@test integrate(x^-1*(d+c*d*x)^2*(a+b*arctanh(c*x)), x) == :(a*d^2*log(x)+b*d^2*log(1+-1*c^2*x^2)+(1/2)*b*d^2*Polylogarithms.polylog(2,c*x)+-1//2*b*d^2*Polylogarithms.polylog(2,-1*c*x)+-1//2*b*d^2*arctanh(c*x)+(1/2)*b*c*x*d^2+(1/2)*c^2*d^2*x^2*(a+b*arctanh(c*x))+2*a*c*x*d^2+2*b*c*x*d^2*arctanh(c*x))
@test integrate(x^-3*(d+c*d*x)^2*(a+b*arctanh(c*x)), x) == :(-1//2*d^2*x^-2*(a+b*arctanh(c*x))+a*c^2*d^2*log(x)+(1/2)*b*c^2*d^2*Polylogarithms.polylog(2,c*x)+(1/2)*b*c^2*d^2*arctanh(c*x)+-1*b*c^2*d^2*log(1+-1*c^2*x^2)+-2*c*d^2*x^-1*(a+b*arctanh(c*x))+2*b*c^2*d^2*log(x)+-1//2*b*c*d^2*x^-1+-1//2*b*c^2*d^2*Polylogarithms.polylog(2,-1*c*x))
@test integrate(x^-4*(d+c*d*x)^2*(a+b*arctanh(c*x)), x) == :(-1*b*c^2*d^2*x^-1+-4//3*b*c^3*d^2*log(1+-1*c*x)+-1//3*d^2*x^-3*(1+c*x)^3*(a+b*arctanh(c*x))+-1//6*b*c*d^2*x^-2+4//3*b*c^3*d^2*log(x))
@test integrate(x^-5*(d+c*d*x)^2*(a+b*arctanh(c*x)), x) == :(-1//4*d^2*x^-4*(a+b*arctanh(c*x))+-17//24*b*c^4*d^2*log(1+-1*c*x)+-3//4*b*c^3*d^2*x^-1+-2//3*c*d^2*x^-3*(a+b*arctanh(c*x))+-1//2*c^2*d^2*x^-2*(a+b*arctanh(c*x))+-1//3*b*c^2*d^2*x^-2+-1//12*b*c*d^2*x^-3+1//24*b*c^4*d^2*log(1+c*x)+2//3*b*c^4*d^2*log(x))
@test integrate(x^-6*(d+c*d*x)^2*(a+b*arctanh(c*x)), x) == :(-1//5*d^2*x^-5*(a+b*arctanh(c*x))+-31//60*b*c^5*d^2*log(1+-1*c*x)+-4//15*b*c^3*d^2*x^-2+-1//2*b*c^4*d^2*x^-1+-1//2*c*d^2*x^-4*(a+b*arctanh(c*x))+-1//3*c^2*d^2*x^-3*(a+b*arctanh(c*x))+-1//6*b*c^2*d^2*x^-3+-1//20*b*c*d^2*x^-4+-1//60*b*c^5*d^2*log(1+c*x)+8//15*b*c^5*d^2*log(x))
@test integrate(x^3*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(1//4*d^3*x^4*(a+b*arctanh(c*x))+13//70*b*d^3*x^4+(1/2)*c^2*d^3*x^6*(a+b*arctanh(c*x))+-1//280*b*c^-4*d^3*log(1+c*x)+1//4*b*c^-1*d^3*x^3+1//7*c^3*d^3*x^7*(a+b*arctanh(c*x))+1//10*b*c*d^3*x^5+1//42*b*c^2*d^3*x^6+3//4*b*x*c^-3*d^3+3//5*c*d^3*x^5*(a+b*arctanh(c*x))+13//35*b*c^-2*d^3*x^2+209//280*b*c^-4*d^3*log(1+-1*c*x))
@test integrate(x^2*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(1//3*d^3*x^3*(a+b*arctanh(c*x))+11//36*b*d^3*x^3+1//6*c^3*d^3*x^6*(a+b*arctanh(c*x))+1//30*b*c^2*d^3*x^5+1//120*b*c^-3*d^3*log(1+c*x)+3//4*c*d^3*x^4*(a+b*arctanh(c*x))+3//5*c^2*d^3*x^5*(a+b*arctanh(c*x))+3//20*b*c*d^3*x^4+7//15*b*c^-1*d^3*x^2+11//12*b*x*c^-2*d^3+37//40*b*c^-3*d^3*log(1+-1*c*x))
@test integrate(x*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(-1//4*c^-2*d^3*(1+c*x)^4*(a+b*arctanh(c*x))+1//5*c^-2*d^3*(1+c*x)^5*(a+b*arctanh(c*x))+1//20*b*c^-2*d^3*(1+c*x)^3+1//20*b*c^-2*d^3*(1+c*x)^4+3//5*b*x*c^-1*d^3+3//20*b*c^-2*d^3*(1+c*x)^2+6//5*b*c^-2*d^3*log(1+-1*c*x))
@test integrate((d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(b*x*d^3+2*b*c^-1*d^3*log(1+-1*c*x)+1//4*b*c^-1*d^3*(1+c*x)^2+1//4*c^-1*d^3*(1+c*x)^4*(a+b*arctanh(c*x))+1//12*b*c^-1*d^3*(1+c*x)^3)
@test integrate(x^-1*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(a*d^3*log(x)+(1/2)*b*d^3*Polylogarithms.polylog(2,c*x)+-3//2*b*d^3*arctanh(c*x)+-1//2*b*d^3*Polylogarithms.polylog(2,-1*c*x)+5//3*b*d^3*log(1+-1*c^2*x^2)+3*a*c*x*d^3+1//3*c^3*d^3*x^3*(a+b*arctanh(c*x))+1//6*b*c^2*d^3*x^2+3//2*b*c*x*d^3+3//2*c^2*d^3*x^2*(a+b*arctanh(c*x))+3*b*c*x*d^3*arctanh(c*x))
@test integrate(x^-2*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(-1*d^3*x^-1*(a+b*arctanh(c*x))+b*c*d^3*log(x)+b*c*d^3*log(1+-1*c^2*x^2)+(1/2)*b*x*c^2*d^3+(1/2)*c^3*d^3*x^2*(a+b*arctanh(c*x))+3*a*c*d^3*log(x)+3*a*x*c^2*d^3+-3//2*b*c*d^3*Polylogarithms.polylog(2,-1*c*x)+-1//2*b*c*d^3*arctanh(c*x)+3//2*b*c*d^3*Polylogarithms.polylog(2,c*x)+3*b*x*c^2*d^3*arctanh(c*x))
@test integrate(x^-3*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(-1//2*d^3*x^-2*(a+b*arctanh(c*x))+a*x*c^3*d^3+(1/2)*b*c^2*d^3*arctanh(c*x)+-1*b*c^2*d^3*log(1+-1*c^2*x^2)+-3*c*d^3*x^-1*(a+b*arctanh(c*x))+3*a*c^2*d^3*log(x)+3*b*c^2*d^3*log(x)+-3//2*b*c^2*d^3*Polylogarithms.polylog(2,-1*c*x)+-1//2*b*c*d^3*x^-1+3//2*b*c^2*d^3*Polylogarithms.polylog(2,c*x)+b*x*c^3*d^3*arctanh(c*x))
@test integrate(x^-4*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(-1//3*d^3*x^-3*(a+b*arctanh(c*x))+a*c^3*d^3*log(x)+(1/2)*b*c^3*d^3*Polylogarithms.polylog(2,c*x)+-3*c^2*d^3*x^-1*(a+b*arctanh(c*x))+-5//3*b*c^3*d^3*log(1+-1*c^2*x^2)+-3//2*b*c^2*d^3*x^-1+-3//2*c*d^3*x^-2*(a+b*arctanh(c*x))+-1//2*b*c^3*d^3*Polylogarithms.polylog(2,-1*c*x)+-1//6*b*c*d^3*x^-2+3//2*b*c^3*d^3*arctanh(c*x)+10//3*b*c^3*d^3*log(x))
@test integrate(x^-5*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(-2*b*c^4*d^3*log(1+-1*c*x)+2*b*c^4*d^3*log(x)+-7//4*b*c^3*d^3*x^-1+-1//2*b*c^2*d^3*x^-2+-1//4*d^3*x^-4*(1+c*x)^4*(a+b*arctanh(c*x))+-1//12*b*c*d^3*x^-3)
@test integrate(x^-6*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(-6//5*b*c^5*d^3*log(1+-1*c*x)+-5//4*b*c^4*d^3*x^-1+-3//5*b*c^3*d^3*x^-2+-1//4*b*c^2*d^3*x^-3+-1//5*d^3*x^-5*(1+c*x)^4*(a+b*arctanh(c*x))+-1//20*b*c*d^3*x^-4+6//5*b*c^5*d^3*log(x)+1//20*c*d^3*x^-4*(1+c*x)^4*(a+b*arctanh(c*x)))
@test integrate(x^-7*(d+c*d*x)^3*(a+b*arctanh(c*x)), x) == :(-1//6*d^3*x^-6*(a+b*arctanh(c*x))+-37//40*b*c^6*d^3*log(1+-1*c*x)+-11//12*b*c^5*d^3*x^-1+-11//36*b*c^3*d^3*x^-3+-7//15*b*c^4*d^3*x^-2+-3//4*c^2*d^3*x^-4*(a+b*arctanh(c*x))+-3//5*c*d^3*x^-5*(a+b*arctanh(c*x))+-3//20*b*c^2*d^3*x^-4+-1//3*c^3*d^3*x^-3*(a+b*arctanh(c*x))+-1//30*b*c*d^3*x^-5+-1//120*b*c^6*d^3*log(1+c*x)+14//15*b*c^6*d^3*log(x))
@test integrate(x^3*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(1//4*d^4*x^4*(a+b*arctanh(c*x))+12//35*b*d^4*x^4+c^2*d^4*x^6*(a+b*arctanh(c*x))+-1//560*b*c^-4*d^4*log(1+c*x)+1//8*c^4*d^4*x^8*(a+b*arctanh(c*x))+1//56*b*c^3*d^4*x^7+2//21*b*c^2*d^4*x^6+4//5*c*d^4*x^5*(a+b*arctanh(c*x))+4//7*c^3*d^4*x^7*(a+b*arctanh(c*x))+9//40*b*c*d^4*x^5+11//8*b*x*c^-3*d^4+11//24*b*c^-1*d^4*x^3+24//35*b*c^-2*d^4*x^2+769//560*b*c^-4*d^4*log(1+-1*c*x))
@test integrate(x^2*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(5//9*b*d^4*x^3+-1//3*c^-3*d^4*(1+c*x)^6*(a+b*arctanh(c*x))+1//5*c^-3*d^4*(1+c*x)^5*(a+b*arctanh(c*x))+1//7*c^-3*d^4*(1+c*x)^7*(a+b*arctanh(c*x))+1//42*b*c^3*d^4*x^6+2//15*b*c^2*d^4*x^5+5//3*b*x*c^-2*d^4+47//140*b*c*d^4*x^4+88//105*b*c^-1*d^4*x^2+176//105*b*c^-3*d^4*log(1+-1*c*x))
@test integrate(x*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(-1//5*c^-2*d^4*(1+c*x)^5*(a+b*arctanh(c*x))+1//6*c^-2*d^4*(1+c*x)^6*(a+b*arctanh(c*x))+1//30*b*c^-2*d^4*(1+c*x)^4+1//30*b*c^-2*d^4*(1+c*x)^5+4//15*b*c^-2*d^4*(1+c*x)^2+4//45*b*c^-2*d^4*(1+c*x)^3+16//15*b*x*c^-1*d^4+32//15*b*c^-2*d^4*log(1+-1*c*x))
@test integrate((d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(8//5*b*x*d^4+1//5*c^-1*d^4*(1+c*x)^5*(a+b*arctanh(c*x))+1//20*b*c^-1*d^4*(1+c*x)^4+2//5*b*c^-1*d^4*(1+c*x)^2+2//15*b*c^-1*d^4*(1+c*x)^3+16//5*b*c^-1*d^4*log(1+-1*c*x))
@test integrate(x^-1*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(a*d^4*log(x)+(1/2)*b*d^4*Polylogarithms.polylog(2,c*x)+-13//4*b*d^4*arctanh(c*x)+-1//2*b*d^4*Polylogarithms.polylog(2,-1*c*x)+8//3*b*d^4*log(1+-1*c^2*x^2)+3*c^2*d^4*x^2*(a+b*arctanh(c*x))+4*a*c*x*d^4+1//4*c^4*d^4*x^4*(a+b*arctanh(c*x))+1//12*b*c^3*d^4*x^3+2//3*b*c^2*d^4*x^2+4//3*c^3*d^4*x^3*(a+b*arctanh(c*x))+13//4*b*c*x*d^4+4*b*c*x*d^4*arctanh(c*x))
@test integrate(x^-2*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(-1*d^4*x^-1*(a+b*arctanh(c*x))+b*c*d^4*log(x)+-2*b*c*d^4*Polylogarithms.polylog(2,-1*c*x)+-2*b*c*d^4*arctanh(c*x)+2*b*c*d^4*Polylogarithms.polylog(2,c*x)+2*b*x*c^2*d^4+2*c^3*d^4*x^2*(a+b*arctanh(c*x))+4*a*c*d^4*log(x)+6*a*x*c^2*d^4+1//3*c^4*d^4*x^3*(a+b*arctanh(c*x))+1//6*b*c^3*d^4*x^2+8//3*b*c*d^4*log(1+-1*c^2*x^2)+6*b*x*c^2*d^4*arctanh(c*x))
@test integrate(x^-3*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(-1//2*d^4*x^-2*(a+b*arctanh(c*x))+(1/2)*b*x*c^3*d^4+(1/2)*c^4*d^4*x^2*(a+b*arctanh(c*x))+-4*c*d^4*x^-1*(a+b*arctanh(c*x))+-3*b*c^2*d^4*Polylogarithms.polylog(2,-1*c*x)+3*b*c^2*d^4*Polylogarithms.polylog(2,c*x)+4*a*x*c^3*d^4+4*b*c^2*d^4*log(x)+6*a*c^2*d^4*log(x)+-1//2*b*c*d^4*x^-1+4*b*x*c^3*d^4*arctanh(c*x))
@test integrate(x^-4*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(-1//3*d^4*x^-3*(a+b*arctanh(c*x))+a*x*c^4*d^4+-6*c^2*d^4*x^-1*(a+b*arctanh(c*x))+-2*b*c^2*d^4*x^-1+-2*b*c^3*d^4*Polylogarithms.polylog(2,-1*c*x)+-2*c*d^4*x^-2*(a+b*arctanh(c*x))+2*b*c^3*d^4*Polylogarithms.polylog(2,c*x)+2*b*c^3*d^4*arctanh(c*x)+4*a*c^3*d^4*log(x)+-8//3*b*c^3*d^4*log(1+-1*c^2*x^2)+-1//6*b*c*d^4*x^-2+19//3*b*c^3*d^4*log(x)+b*x*c^4*d^4*arctanh(c*x))
@test integrate(x^-5*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(-1//4*d^4*x^-4*(a+b*arctanh(c*x))+a*c^4*d^4*log(x)+(1/2)*b*c^4*d^4*Polylogarithms.polylog(2,c*x)+-4*c^3*d^4*x^-1*(a+b*arctanh(c*x))+-3*c^2*d^4*x^-2*(a+b*arctanh(c*x))+-13//4*b*c^3*d^4*x^-1+-8//3*b*c^4*d^4*log(1+-1*c^2*x^2)+-4//3*c*d^4*x^-3*(a+b*arctanh(c*x))+-2//3*b*c^2*d^4*x^-2+-1//2*b*c^4*d^4*Polylogarithms.polylog(2,-1*c*x)+-1//12*b*c*d^4*x^-3+13//4*b*c^4*d^4*arctanh(c*x)+16//3*b*c^4*d^4*log(x))
@test integrate(x^-6*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(-3*b*c^4*d^4*x^-1+-16//5*b*c^5*d^4*log(1+-1*c*x)+-11//10*b*c^3*d^4*x^-2+-1//3*b*c^2*d^4*x^-3+-1//5*d^4*x^-5*(1+c*x)^5*(a+b*arctanh(c*x))+-1//20*b*c*d^4*x^-4+16//5*b*c^5*d^4*log(x))
@test integrate(x^-7*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(-32//15*b*c^6*d^4*log(1+-1*c*x)+-16//15*b*c^4*d^4*x^-2+-13//6*b*c^5*d^4*x^-1+-5//9*b*c^3*d^4*x^-3+-1//5*b*c^2*d^4*x^-4+-1//6*d^4*x^-6*(1+c*x)^5*(a+b*arctanh(c*x))+-1//30*b*c*d^4*x^-5+32//15*b*c^6*d^4*log(x)+1//30*c*d^4*x^-5*(1+c*x)^5*(a+b*arctanh(c*x)))
@test integrate(x^-8*(d+c*d*x)^4*(a+b*arctanh(c*x)), x) == :(-1//7*d^4*x^-7*(a+b*arctanh(c*x))+-1*c^3*d^4*x^-4*(a+b*arctanh(c*x))+-117//70*b*c^7*d^4*log(1+-1*c*x)+-88//105*b*c^5*d^4*x^-2+-47//140*b*c^3*d^4*x^-4+-6//5*c^2*d^4*x^-5*(a+b*arctanh(c*x))+-5//3*b*c^6*d^4*x^-1+-5//9*b*c^4*d^4*x^-3+-2//3*c*d^4*x^-6*(a+b*arctanh(c*x))+-2//15*b*c^2*d^4*x^-5+-1//3*c^4*d^4*x^-3*(a+b*arctanh(c*x))+-1//42*b*c*d^4*x^-6+-1//210*b*c^7*d^4*log(1+c*x)+176//105*b*c^7*d^4*log(x))
@test integrate(x^3*(d+c*d*x)^-1*(a+b*arctanh(c*x)), x) == :(a*x*c^-3*d^-1+c^-4*d^-1*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*c^-4*d^-1*arctanh(c*x)+-1//2*b*x*c^-3*d^-1+-1//2*b*c^-4*d^-1*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1//2*c^-2*d^-1*x^2*(a+b*arctanh(c*x))+1//3*c^-1*d^-1*x^3*(a+b*arctanh(c*x))+1//6*b*c^-2*d^-1*x^2+2//3*b*c^-4*d^-1*log(1+-1*c^2*x^2)+b*x*c^-3*d^-1*arctanh(c*x))
@test integrate(x^2*(d+c*d*x)^-1*(a+b*arctanh(c*x)), x) == :((1/2)*b*x*c^-2*d^-1+(1/2)*b*c^-3*d^-1*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+(1/2)*c^-1*d^-1*x^2*(a+b*arctanh(c*x))+-1*a*x*c^-2*d^-1+-1*c^-3*d^-1*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-1//2*b*c^-3*d^-1*arctanh(c*x)+-1//2*b*c^-3*d^-1*log(1+-1*c^2*x^2)+-1*b*x*c^-2*d^-1*arctanh(c*x))
@test integrate(x*(d+c*d*x)^-1*(a+b*arctanh(c*x)), x) == :(a*x*c^-1*d^-1+c^-2*d^-1*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*c^-2*d^-1*log(1+-1*c^2*x^2)+-1//2*b*c^-2*d^-1*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+b*x*c^-1*d^-1*arctanh(c*x))
@test integrate((d+c*d*x)^-1*(a+b*arctanh(c*x)), x) == :((1/2)*b*c^-1*d^-1*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*c^-1*d^-1*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1))
@test integrate(x^-1*(d+c*d*x)^-1*(a+b*arctanh(c*x)), x) == :(d^-1*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1)+-1//2*b*d^-1*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1))
@test integrate(x^-2*(d+c*d*x)^-1*(a+b*arctanh(c*x)), x) == :(-1*d^-1*x^-1*(a+b*arctanh(c*x))+b*c*d^-1*log(x)+(1/2)*b*c*d^-1*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1*c*d^-1*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1)+-1//2*b*c*d^-1*log(1+-1*c^2*x^2))
@test integrate(x^-3*(d+c*d*x)^-1*(a+b*arctanh(c*x)), x) == :(-1//2*d^-1*x^-2*(a+b*arctanh(c*x))+c*d^-1*x^-1*(a+b*arctanh(c*x))+c^2*d^-1*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1)+(1/2)*b*c^2*d^-1*arctanh(c*x)+(1/2)*b*c^2*d^-1*log(1+-1*c^2*x^2)+-1*b*c^2*d^-1*log(x)+-1//2*b*c*d^-1*x^-1+-1//2*b*c^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1))
@test integrate(x^-4*(d+c*d*x)^-1*(a+b*arctanh(c*x)), x) == :(-1//3*d^-1*x^-3*(a+b*arctanh(c*x))+(1/2)*b*c^2*d^-1*x^-1+(1/2)*b*c^3*d^-1*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+(1/2)*c*d^-1*x^-2*(a+b*arctanh(c*x))+-1*c^2*d^-1*x^-1*(a+b*arctanh(c*x))+-1*c^3*d^-1*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1)+-2//3*b*c^3*d^-1*log(1+-1*c^2*x^2)+-1//2*b*c^3*d^-1*arctanh(c*x)+-1//6*b*c*d^-1*x^-2+4//3*b*c^3*d^-1*log(x))
@test integrate(x^3*(d+c*d*x)^-2*(a+b*arctanh(c*x)), x) == :(c^-4*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+(1/2)*b*x*c^-3*d^-2+(1/2)*b*c^-4*d^-2*(1+c*x)^-1+(1/2)*c^-2*d^-2*x^2*(a+b*arctanh(c*x))+-1*b*c^-4*d^-2*arctanh(c*x)+-1*b*c^-4*d^-2*log(1+-1*c^2*x^2)+-1*c^-4*d^-2*(3a+3*b*arctanh(c*x))*log(2*(1+c*x)^-1)+-2*a*x*c^-3*d^-2+3//2*b*c^-4*d^-2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-2*b*x*c^-3*d^-2*arctanh(c*x))
@test integrate(x^2*(d+c*d*x)^-2*(a+b*arctanh(c*x)), x) == :(a*x*c^-2*d^-2+c^-3*d^-2*(2a+2*b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*c^-3*d^-2*arctanh(c*x)+(1/2)*b*c^-3*d^-2*log(1+-1*c^2*x^2)+-1*b*c^-3*d^-2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*c^-3*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+-1//2*b*c^-3*d^-2*(1+c*x)^-1+b*x*c^-2*d^-2*arctanh(c*x))
@test integrate(x*(d+c*d*x)^-2*(a+b*arctanh(c*x)), x) == :(c^-2*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+(1/2)*b*c^-2*d^-2*(1+c*x)^-1+(1/2)*b*c^-2*d^-2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*c^-2*d^-2*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-1//2*b*c^-2*d^-2*arctanh(c*x))
@test integrate((d+c*d*x)^-2*(a+b*arctanh(c*x)), x) == :((1/2)*b*c^-1*d^-2*arctanh(c*x)+-1*c^-1*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+-1//2*b*c^-1*d^-2*(1+c*x)^-1)
@test integrate(x^-1*(d+c*d*x)^-2*(a+b*arctanh(c*x)), x) == :(a*d^-2*log(x)+d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+d^-2*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*d^-2*(1+c*x)^-1+(1/2)*b*d^-2*Polylogarithms.polylog(2,c*x)+-1//2*b*d^-2*Polylogarithms.polylog(2,-1*c*x)+-1//2*b*d^-2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1//2*b*d^-2*arctanh(c*x))
@test integrate(x^-2*(d+c*d*x)^-2*(a+b*arctanh(c*x)), x) == :(-1*d^-2*x^-1*(a+b*arctanh(c*x))+b*c*d^-2*Polylogarithms.polylog(2,-1*c*x)+b*c*d^-2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+b*c*d^-2*log(x)+(1/2)*b*c*d^-2*arctanh(c*x)+-1*b*c*d^-2*Polylogarithms.polylog(2,c*x)+-1*c*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+-2*a*c*d^-2*log(x)+-2*c*d^-2*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-1//2*b*c*d^-2*(1+c*x)^-1+-1//2*b*c*d^-2*log(1+-1*c^2*x^2))
@test integrate(x^-3*(d+c*d*x)^-2*(a+b*arctanh(c*x)), x) == :(-1//2*d^-2*x^-2*(a+b*arctanh(c*x))+b*c^2*d^-2*log(1+-1*c^2*x^2)+c^2*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+(1/2)*b*c^2*d^-2*(1+c*x)^-1+-2*b*c^2*d^-2*log(x)+2*c*d^-2*x^-1*(a+b*arctanh(c*x))+3*a*c^2*d^-2*log(x)+3*c^2*d^-2*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-3//2*b*c^2*d^-2*Polylogarithms.polylog(2,-1*c*x)+-3//2*b*c^2*d^-2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1//2*b*c*d^-2*x^-1+3//2*b*c^2*d^-2*Polylogarithms.polylog(2,c*x))
@test integrate(x^4*(d+c*d*x)^-3*(a+b*arctanh(c*x)), x) == :(c^-5*d^-3*(1+c*x)^-1*(4a+4*b*arctanh(c*x))+(1/2)*b*x*c^-4*d^-3+(1/2)*c^-3*d^-3*x^2*(a+b*arctanh(c*x))+-1*c^-5*d^-3*(6a+6*b*arctanh(c*x))*log(2*(1+c*x)^-1)+-3*a*x*c^-4*d^-3+3*b*c^-5*d^-3*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-19//8*b*c^-5*d^-3*arctanh(c*x)+-3//2*b*c^-5*d^-3*log(1+-1*c^2*x^2)+-1//2*c^-5*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+-1//8*b*c^-5*d^-3*(1+c*x)^-2+15//8*b*c^-5*d^-3*(1+c*x)^-1+-3*b*x*c^-4*d^-3*arctanh(c*x))
@test integrate(x^3*(d+c*d*x)^-3*(a+b*arctanh(c*x)), x) == :(a*x*c^-3*d^-3+c^-4*d^-3*(3a+3*b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*c^-4*d^-3*log(1+-1*c^2*x^2)+(1/2)*c^-4*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+-1*c^-4*d^-3*(1+c*x)^-1*(3a+3*b*arctanh(c*x))+-11//8*b*c^-4*d^-3*(1+c*x)^-1+-3//2*b*c^-4*d^-3*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+1//8*b*c^-4*d^-3*(1+c*x)^-2+11//8*b*c^-4*d^-3*arctanh(c*x)+b*x*c^-3*d^-3*arctanh(c*x))
@test integrate(x^2*(d+c*d*x)^-3*(a+b*arctanh(c*x)), x) == :(c^-3*d^-3*(1+c*x)^-1*(2a+2*b*arctanh(c*x))+(1/2)*b*c^-3*d^-3*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*c^-3*d^-3*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-7//8*b*c^-3*d^-3*arctanh(c*x)+-1//2*c^-3*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+-1//8*b*c^-3*d^-3*(1+c*x)^-2+7//8*b*c^-3*d^-3*(1+c*x)^-1)
@test integrate(x*(d+c*d*x)^-3*(a+b*arctanh(c*x)), x) == :((1/2)*d^-3*x^2*(1+c*x)^-2*(a+b*arctanh(c*x))+-3//8*b*c^-2*d^-3*(1+c*x)^-1+-1//8*b*c^-2*d^-3*arctanh(c*x)+1//8*b*c^-2*d^-3*(1+c*x)^-2)
@test integrate((d+c*d*x)^-3*(a+b*arctanh(c*x)), x) == :(-1//2*c^-1*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+-1//8*b*c^-1*d^-3*(1+c*x)^-1+-1//8*b*c^-1*d^-3*(1+c*x)^-2+1//8*b*c^-1*d^-3*arctanh(c*x))
@test integrate(x^-1*(d+c*d*x)^-3*(a+b*arctanh(c*x)), x) == :(a*d^-3*log(x)+d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))+d^-3*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*d^-3*Polylogarithms.polylog(2,c*x)+(1/2)*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+-5//8*b*d^-3*arctanh(c*x)+-1//2*b*d^-3*Polylogarithms.polylog(2,-1*c*x)+-1//2*b*d^-3*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+1//8*b*d^-3*(1+c*x)^-2+5//8*b*d^-3*(1+c*x)^-1)
@test integrate(x^-2*(d+c*d*x)^-3*(a+b*arctanh(c*x)), x) == :(-1*d^-3*x^-1*(a+b*arctanh(c*x))+b*c*d^-3*log(x)+-3*a*c*d^-3*log(x)+-3*c*d^-3*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-2*c*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))+-9//8*b*c*d^-3*(1+c*x)^-1+-3//2*b*c*d^-3*Polylogarithms.polylog(2,c*x)+-1//2*b*c*d^-3*log(1+-1*c^2*x^2)+-1//2*c*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+-1//8*b*c*d^-3*(1+c*x)^-2+3//2*b*c*d^-3*Polylogarithms.polylog(2,-1*c*x)+3//2*b*c*d^-3*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+9//8*b*c*d^-3*arctanh(c*x))
@test integrate(x^-3*(d+c*d*x)^-3*(a+b*arctanh(c*x)), x) == :(-1//2*d^-3*x^-2*(a+b*arctanh(c*x))+(1/2)*c^2*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+-3*b*c^2*d^-3*Polylogarithms.polylog(2,-1*c*x)+-3*b*c^2*d^-3*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-3*b*c^2*d^-3*log(x)+3*b*c^2*d^-3*Polylogarithms.polylog(2,c*x)+3*c*d^-3*x^-1*(a+b*arctanh(c*x))+3*c^2*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))+6*a*c^2*d^-3*log(x)+6*c^2*d^-3*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-9//8*b*c^2*d^-3*arctanh(c*x)+-1//2*b*c*d^-3*x^-1+1//8*b*c^2*d^-3*(1+c*x)^-2+3//2*b*c^2*d^-3*log(1+-1*c^2*x^2)+13//8*b*c^2*d^-3*(1+c*x)^-1)
@test integrate((1+c*x)^-4*(a+b*arctanh(c*x)), x) == :(-1//3*c^-1*(1+c*x)^-3*(a+b*arctanh(c*x))+-1//18*b*c^-1*(1+c*x)^-3+-1//24*b*c^-1*(1+c*x)^-1+-1//24*b*c^-1*(1+c*x)^-2+1//24*b*c^-1*arctanh(c*x))
@test integrate((c*x+a*c*x^2)^-1*arctanh(a*x), x) == :(-1//2*c^-1*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+c^-1*arctanh(a*x)*log(2+-2*(1+a*x)^-1))
@test integrate(x^3*(a+b*arctanh(c*x))^2*(d+c*d*x), x) == :(-1//20*d*c^-4*(a+b*arctanh(c*x))^2+1//4*d*x^4*(a+b*arctanh(c*x))^2+-3//10*d*b^2*c^-4*arctanh(c*x)+-1//5*d*b^2*c^-4*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//3*d*b^2*c^-4*log(1+-1*c^2*x^2)+1//5*c*d*x^5*(a+b*arctanh(c*x))^2+1//10*b*d*x^4*(a+b*arctanh(c*x))+1//12*d*b^2*c^-2*x^2+1//30*d*b^2*c^-1*x^3+3//10*d*x*b^2*c^-3+(1/2)*a*b*d*x*c^-3+(1/2)*d*x*b^2*c^-3*arctanh(c*x)+-2//5*b*d*c^-4*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//5*b*d*c^-2*x^2*(a+b*arctanh(c*x))+1//6*b*d*c^-1*x^3*(a+b*arctanh(c*x)))
@test integrate(x^2*(a+b*arctanh(c*x))^2*(d+c*d*x), x) == :(1//3*d*x^3*(a+b*arctanh(c*x))^2+1//12*d*c^-3*(a+b*arctanh(c*x))^2+-1//3*d*b^2*c^-3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//3*d*b^2*c^-3*arctanh(c*x)+1//3*d*x*b^2*c^-2+1//3*d*b^2*c^-3*log(1+-1*c^2*x^2)+1//4*c*d*x^4*(a+b*arctanh(c*x))^2+1//6*b*d*x^3*(a+b*arctanh(c*x))+1//12*d*b^2*c^-1*x^2+(1/2)*a*b*d*x*c^-2+(1/2)*d*x*b^2*c^-2*arctanh(c*x)+-2//3*b*d*c^-3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//3*b*d*c^-1*x^2*(a+b*arctanh(c*x)))
@test integrate(x*(a+b*arctanh(c*x))^2*(d+c*d*x), x) == :((1/2)*d*x^2*(a+b*arctanh(c*x))^2+-1//6*d*c^-2*(a+b*arctanh(c*x))^2+(1/2)*d*b^2*c^-2*log(1+-1*c^2*x^2)+-1//3*d*b^2*c^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//3*d*b^2*c^-2*arctanh(c*x)+1//3*b*d*x^2*(a+b*arctanh(c*x))+1//3*c*d*x^3*(a+b*arctanh(c*x))^2+1//3*d*x*b^2*c^-1+a*b*d*x*c^-1+d*x*b^2*c^-1*arctanh(c*x)+-2//3*b*d*c^-2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate((a+b*arctanh(c*x))^2*(d+c*d*x), x) == :(a*b*d*x+d*x*b^2*arctanh(c*x)+(1/2)*d*b^2*c^-1*log(1+-1*c^2*x^2)+(1/2)*d*c^-1*(1+c*x)^2*(a+b*arctanh(c*x))^2+-1*d*b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-2*b*d*c^-1*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x))^2*(d+c*d*x), x) == :(d*(a+b*arctanh(c*x))^2+(1/2)*d*b^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-1*d*b^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+2*d*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-1//2*d*b^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+b*d*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+c*d*x*(a+b*arctanh(c*x))^2+-1*b*d*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-2*b*d*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x^-2*(a+b*arctanh(c*x))^2*(d+c*d*x), x) == :(c*d*(a+b*arctanh(c*x))^2+-1*d*x^-1*(a+b*arctanh(c*x))^2+(1/2)*c*d*b^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-1*c*d*b^2*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+2*c*d*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-1//2*c*d*b^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+b*c*d*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+-1*b*c*d*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+2*b*c*d*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x))^2*(d+c*d*x), x) == :(-1//2*d*x^-2*(a+b*arctanh(c*x))^2+3//2*d*c^2*(a+b*arctanh(c*x))^2+d*b^2*c^2*log(x)+-1*c*d*x^-1*(a+b*arctanh(c*x))^2+-1*d*b^2*c^2*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1//2*d*b^2*c^2*log(1+-1*c^2*x^2)+-1*b*c*d*x^-1*(a+b*arctanh(c*x))+2*b*d*c^2*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-4*(a+b*arctanh(c*x))^2*(d+c*d*x), x) == :(-1//3*d*x^-3*(a+b*arctanh(c*x))^2+5//6*d*c^3*(a+b*arctanh(c*x))^2+d*b^2*c^3*log(x)+-1//2*c*d*x^-2*(a+b*arctanh(c*x))^2+-1//2*d*b^2*c^3*log(1+-1*c^2*x^2)+-1//3*d*b^2*c^2*x^-1+-1//3*d*b^2*c^3*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+1//3*d*b^2*c^3*arctanh(c*x)+-1*b*d*c^2*x^-1*(a+b*arctanh(c*x))+-1//3*b*c*d*x^-2*(a+b*arctanh(c*x))+2//3*b*d*c^3*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^3*(a+b*arctanh(c*x))^2*(d+c*d*x)^2, x) == :(-1//60*c^-4*d^2*(a+b*arctanh(c*x))^2+1//4*d^2*x^4*(a+b*arctanh(c*x))^2+1//60*b^2*d^2*x^4+-3//5*b^2*c^-4*d^2*arctanh(c*x)+-2//5*b^2*c^-4*d^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//5*b*d^2*x^4*(a+b*arctanh(c*x))+1//6*c^2*d^2*x^6*(a+b*arctanh(c*x))^2+1//15*b^2*c^-1*d^2*x^3+2//5*c*d^2*x^5*(a+b*arctanh(c*x))^2+3//5*x*b^2*c^-3*d^2+31//180*b^2*c^-2*d^2*x^2+53//90*b^2*c^-4*d^2*log(1+-1*c^2*x^2)+-4//5*b*c^-4*d^2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//15*b*c*d^2*x^5*(a+b*arctanh(c*x))+2//5*b*c^-2*d^2*x^2*(a+b*arctanh(c*x))+5//6*a*b*x*c^-3*d^2+5//6*x*b^2*c^-3*d^2*arctanh(c*x)+5//18*b*c^-1*d^2*x^3*(a+b*arctanh(c*x)))
@test integrate(x^2*(a+b*arctanh(c*x))^2*(d+c*d*x)^2, x) == :(1//3*d^2*x^3*(a+b*arctanh(c*x))^2+1//30*b^2*d^2*x^3+1//30*c^-3*d^2*(a+b*arctanh(c*x))^2+(1/2)*c*d^2*x^4*(a+b*arctanh(c*x))^2+-19//30*b^2*c^-3*d^2*arctanh(c*x)+-8//15*b^2*c^-3*d^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//3*b*d^2*x^3*(a+b*arctanh(c*x))+1//5*c^2*d^2*x^5*(a+b*arctanh(c*x))^2+1//6*b^2*c^-1*d^2*x^2+2//3*b^2*c^-3*d^2*log(1+-1*c^2*x^2)+19//30*x*b^2*c^-2*d^2+a*b*x*c^-2*d^2+x*b^2*c^-2*d^2*arctanh(c*x)+-16//15*b*c^-3*d^2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//10*b*c*d^2*x^4*(a+b*arctanh(c*x))+8//15*b*c^-1*d^2*x^2*(a+b*arctanh(c*x)))
@test integrate(x*(a+b*arctanh(c*x))^2*(d+c*d*x)^2, x) == :((1/2)*d^2*x^2*(a+b*arctanh(c*x))^2+-1//12*c^-2*d^2*(a+b*arctanh(c*x))^2+1//12*b^2*d^2*x^2+-2//3*b^2*c^-2*d^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-2//3*b^2*c^-2*d^2*arctanh(c*x)+1//4*c^2*d^2*x^4*(a+b*arctanh(c*x))^2+2//3*b*d^2*x^2*(a+b*arctanh(c*x))+2//3*c*d^2*x^3*(a+b*arctanh(c*x))^2+2//3*x*b^2*c^-1*d^2+5//6*b^2*c^-2*d^2*log(1+-1*c^2*x^2)+-4//3*b*c^-2*d^2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//6*b*c*d^2*x^3*(a+b*arctanh(c*x))+3//2*a*b*x*c^-1*d^2+3//2*x*b^2*c^-1*d^2*arctanh(c*x))
@test integrate((a+b*arctanh(c*x))^2*(d+c*d*x)^2, x) == :(1//3*x*b^2*d^2+b^2*c^-1*d^2*log(1+-1*c^2*x^2)+2*a*b*x*d^2+2*x*b^2*d^2*arctanh(c*x)+-4//3*b^2*c^-1*d^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//3*b^2*c^-1*d^2*arctanh(c*x)+1//3*c^-1*d^2*(1+c*x)^3*(a+b*arctanh(c*x))^2+-8//3*b*c^-1*d^2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//3*b*c*d^2*x^2*(a+b*arctanh(c*x)))
@test integrate(x^-1*(a+b*arctanh(c*x))^2*(d+c*d*x)^2, x) == :(3//2*d^2*(a+b*arctanh(c*x))^2+(1/2)*b^2*d^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+(1/2)*b^2*d^2*log(1+-1*c^2*x^2)+-2*b^2*d^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+2*d^2*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-1//2*b^2*d^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+b*d^2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+(1/2)*c^2*d^2*x^2*(a+b*arctanh(c*x))^2+-1*b*d^2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-4*b*d^2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+2*c*x*d^2*(a+b*arctanh(c*x))^2+a*b*c*x*d^2+c*x*b^2*d^2*arctanh(c*x))
@test integrate(x^-2*(a+b*arctanh(c*x))^2*(d+c*d*x)^2, x) == :(-1*d^2*x^-1*(a+b*arctanh(c*x))^2+2*c*d^2*(a+b*arctanh(c*x))^2+c*b^2*d^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+x*c^2*d^2*(a+b*arctanh(c*x))^2+-1*c*b^2*d^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1*c*b^2*d^2*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1*c*b^2*d^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+4*c*d^2*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-2*b*c*d^2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-2*b*c*d^2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+2*b*c*d^2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+2*b*c*d^2*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x))^2*(d+c*d*x)^2, x) == :(-1//2*d^2*x^-2*(a+b*arctanh(c*x))^2+5//2*c^2*d^2*(a+b*arctanh(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+-1*c*x)^-1)+-2*c*d^2*x^-1*(a+b*arctanh(c*x))^2+-2*b^2*c^2*d^2*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+2*c^2*d^2*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-1//2*b^2*c^2*d^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+-1//2*b^2*c^2*d^2*log(1+-1*c^2*x^2)+b*c^2*d^2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+-1*b*c*d^2*x^-1*(a+b*arctanh(c*x))+-1*b*c^2*d^2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+4*b*c^2*d^2*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-4*(a+b*arctanh(c*x))^2*(d+c*d*x)^2, x) == :(-1*b^2*c^3*d^2*log(1+-1*c^2*x^2)+2*b^2*c^3*d^2*log(x)+-4//3*b^2*c^3*d^2*Polylogarithms.polylog(2,-1*c*x)+-1//3*b^2*c^2*d^2*x^-1+-1//3*d^2*x^-3*(1+c*x)^3*(a+b*arctanh(c*x))^2+1//3*b^2*c^3*d^2*arctanh(c*x)+4//3*b^2*c^3*d^2*Polylogarithms.polylog(2,c*x)+4//3*b^2*c^3*d^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-2*b*c^2*d^2*x^-1*(a+b*arctanh(c*x))+-1//3*b*c*d^2*x^-2*(a+b*arctanh(c*x))+8//3*a*b*c^3*d^2*log(x)+8//3*b*c^3*d^2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x^3*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(-1//140*c^-4*d^3*(a+b*arctanh(c*x))^2+1//4*d^3*x^4*(a+b*arctanh(c*x))^2+1//20*b^2*d^3*x^4+(1/2)*c^2*d^3*x^6*(a+b*arctanh(c*x))^2+-122//105*b^2*c^-4*d^3*arctanh(c*x)+-26//35*b^2*c^-4*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//7*c^3*d^3*x^7*(a+b*arctanh(c*x))^2+1//105*c*b^2*d^3*x^5+3//5*c*d^3*x^5*(a+b*arctanh(c*x))^2+7//20*b^2*c^-2*d^3*x^2+11//10*b^2*c^-4*d^3*log(1+-1*c^2*x^2)+13//35*b*d^3*x^4*(a+b*arctanh(c*x))+44//315*b^2*c^-1*d^3*x^3+122//105*x*b^2*c^-3*d^3+(1/2)*b*c^-1*d^3*x^3*(a+b*arctanh(c*x))+-52//35*b*c^-4*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//5*b*c*d^3*x^5*(a+b*arctanh(c*x))+1//21*b*c^2*d^3*x^6*(a+b*arctanh(c*x))+3//2*a*b*x*c^-3*d^3+3//2*x*b^2*c^-3*d^3*arctanh(c*x)+26//35*b*c^-2*d^3*x^2*(a+b*arctanh(c*x)))
@test integrate(x^2*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(1//3*d^3*x^3*(a+b*arctanh(c*x))^2+1//10*b^2*d^3*x^3+1//60*c^-3*d^3*(a+b*arctanh(c*x))^2+-37//30*b^2*c^-3*d^3*arctanh(c*x)+-14//15*b^2*c^-3*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//6*c^3*d^3*x^6*(a+b*arctanh(c*x))^2+1//60*c*b^2*d^3*x^4+3//4*c*d^3*x^4*(a+b*arctanh(c*x))^2+3//5*c^2*d^3*x^5*(a+b*arctanh(c*x))^2+11//18*b*d^3*x^3*(a+b*arctanh(c*x))+37//30*x*b^2*c^-2*d^3+61//180*b^2*c^-1*d^3*x^2+113//90*b^2*c^-3*d^3*log(1+-1*c^2*x^2)+-28//15*b*c^-3*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//15*b*c^2*d^3*x^5*(a+b*arctanh(c*x))+3//10*b*c*d^3*x^4*(a+b*arctanh(c*x))+11//6*a*b*x*c^-2*d^3+11//6*x*b^2*c^-2*d^3*arctanh(c*x)+14//15*b*c^-1*d^3*x^2*(a+b*arctanh(c*x)))
@test integrate(x*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(1//4*b^2*d^3*x^2+-13//10*b^2*c^-2*d^3*arctanh(c*x)+-6//5*b^2*c^-2*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//4*c^-2*d^3*(1+c*x)^4*(a+b*arctanh(c*x))^2+1//5*c^-2*d^3*(1+c*x)^5*(a+b*arctanh(c*x))^2+1//30*c*b^2*d^3*x^3+3//2*b^2*c^-2*d^3*log(1+-1*c^2*x^2)+6//5*b*d^3*x^2*(a+b*arctanh(c*x))+13//10*x*b^2*c^-1*d^3+(1/2)*b*c*d^3*x^3*(a+b*arctanh(c*x))+-12//5*b*c^-2*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//10*b*c^2*d^3*x^4*(a+b*arctanh(c*x))+5//2*a*b*x*c^-1*d^3+5//2*x*b^2*c^-1*d^3*arctanh(c*x))
@test integrate((a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(x*b^2*d^3+-1*b^2*c^-1*d^3*arctanh(c*x)+-2*b^2*c^-1*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//4*c^-1*d^3*(1+c*x)^4*(a+b*arctanh(c*x))^2+1//12*c*b^2*d^3*x^2+7//2*a*b*x*d^3+7//2*x*b^2*d^3*arctanh(c*x)+11//6*b^2*c^-1*d^3*log(1+-1*c^2*x^2)+b*c*d^3*x^2*(a+b*arctanh(c*x))+-4*b*c^-1*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//6*b*c^2*d^3*x^3*(a+b*arctanh(c*x)))
@test integrate(x^-1*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(11//6*d^3*(a+b*arctanh(c*x))^2+(1/2)*b^2*d^3*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+2*d^3*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-10//3*b^2*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//2*b^2*d^3*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+-1//3*b^2*d^3*arctanh(c*x)+3//2*b^2*d^3*log(1+-1*c^2*x^2)+b*d^3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+-1*b*d^3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+3*c*x*d^3*(a+b*arctanh(c*x))^2+-20//3*b*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//3*c*x*b^2*d^3+1//3*c^3*d^3*x^3*(a+b*arctanh(c*x))^2+3//2*c^2*d^3*x^2*(a+b*arctanh(c*x))^2+3*a*b*c*x*d^3+3*c*x*b^2*d^3*arctanh(c*x)+1//3*b*c^2*d^3*x^2*(a+b*arctanh(c*x)))
@test integrate(x^-2*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(-1*d^3*x^-1*(a+b*arctanh(c*x))^2+7//2*c*d^3*(a+b*arctanh(c*x))^2+(1/2)*c*b^2*d^3*log(1+-1*c^2*x^2)+(1/2)*c^3*d^3*x^2*(a+b*arctanh(c*x))^2+-1*c*b^2*d^3*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-3*c*b^2*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+3*x*c^2*d^3*(a+b*arctanh(c*x))^2+6*c*d^3*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-3//2*c*b^2*d^3*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+3//2*c*b^2*d^3*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+a*b*x*c^2*d^3+x*b^2*c^2*d^3*arctanh(c*x)+-6*b*c*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+-3*b*c*d^3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+2*b*c*d^3*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1)+3*b*c*d^3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(-1//2*d^3*x^-2*(a+b*arctanh(c*x))^2+9//2*c^2*d^3*(a+b*arctanh(c*x))^2+x*c^3*d^3*(a+b*arctanh(c*x))^2+b^2*c^2*d^3*log(x)+-1*b^2*c^2*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-3*c*d^3*x^-1*(a+b*arctanh(c*x))^2+-3*b^2*c^2*d^3*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+6*c^2*d^3*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-3//2*b^2*c^2*d^3*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+-1//2*b^2*c^2*d^3*log(1+-1*c^2*x^2)+3//2*b^2*c^2*d^3*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-1*b*c*d^3*x^-1*(a+b*arctanh(c*x))+-3*b*c^2*d^3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-2*b*c^2*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+3*b*c^2*d^3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+6*b*c^2*d^3*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-4*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(-1//3*d^3*x^-3*(a+b*arctanh(c*x))^2+29//6*c^3*d^3*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^3*d^3*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-3*c^2*d^3*x^-1*(a+b*arctanh(c*x))^2+2*c^3*d^3*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+3*b^2*c^3*d^3*log(x)+-10//3*b^2*c^3*d^3*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-3//2*c*d^3*x^-2*(a+b*arctanh(c*x))^2+-3//2*b^2*c^3*d^3*log(1+-1*c^2*x^2)+-1//2*b^2*c^3*d^3*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+-1//3*b^2*c^2*d^3*x^-1+1//3*b^2*c^3*d^3*arctanh(c*x)+b*c^3*d^3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+-1*b*c^3*d^3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-3*b*c^2*d^3*x^-1*(a+b*arctanh(c*x))+-1//3*b*c*d^3*x^-2*(a+b*arctanh(c*x))+20//3*b*c^3*d^3*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-5*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(b^2*c^4*d^3*arctanh(c*x)+-1*b^2*c^3*d^3*x^-1+-2*b^2*c^4*d^3*Polylogarithms.polylog(2,-1*c*x)+2*b^2*c^4*d^3*Polylogarithms.polylog(2,c*x)+2*b^2*c^4*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-11//6*b^2*c^4*d^3*log(1+-1*c^2*x^2)+-1//4*d^3*x^-4*(1+c*x)^4*(a+b*arctanh(c*x))^2+-1//12*b^2*c^2*d^3*x^-2+11//3*b^2*c^4*d^3*log(x)+-1*b*c^2*d^3*x^-2*(a+b*arctanh(c*x))+4*a*b*c^4*d^3*log(x)+4*b*c^4*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+-7//2*b*c^3*d^3*x^-1*(a+b*arctanh(c*x))+-1//6*b*c*d^3*x^-3*(a+b*arctanh(c*x)))
@test integrate(x^-6*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(3*b^2*c^5*d^3*log(x)+-13//10*b^2*c^4*d^3*x^-1+-6//5*b^2*c^5*d^3*Polylogarithms.polylog(2,-1*c*x)+-3//2*b^2*c^5*d^3*log(1+-1*c^2*x^2)+-1//4*b^2*c^3*d^3*x^-2+-1//5*d^3*x^-5*(1+c*x)^4*(a+b*arctanh(c*x))^2+-1//30*b^2*c^2*d^3*x^-3+6//5*b^2*c^5*d^3*Polylogarithms.polylog(2,c*x)+6//5*b^2*c^5*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+13//10*b^2*c^5*d^3*arctanh(c*x)+-6//5*b*c^3*d^3*x^-2*(a+b*arctanh(c*x))+-5//2*b*c^4*d^3*x^-1*(a+b*arctanh(c*x))+-1//2*b*c^2*d^3*x^-3*(a+b*arctanh(c*x))+-1//10*b*c*d^3*x^-4*(a+b*arctanh(c*x))+1//20*c*d^3*x^-4*(1+c*x)^4*(a+b*arctanh(c*x))^2+12//5*a*b*c^5*d^3*log(x)+12//5*b*c^5*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x^-7*(a+b*arctanh(c*x))^2*(d+c*d*x)^3, x) == :(-1//6*d^3*x^-6*(a+b*arctanh(c*x))^2+-113//90*b^2*c^6*d^3*log(1+-1*c^2*x^2)+-61//180*b^2*c^4*d^3*x^-2+-37//30*b^2*c^5*d^3*x^-1+-14//15*b^2*c^6*d^3*Polylogarithms.polylog(2,-1*c*x)+-3//4*c^2*d^3*x^-4*(a+b*arctanh(c*x))^2+-3//5*c*d^3*x^-5*(a+b*arctanh(c*x))^2+-1//3*c^3*d^3*x^-3*(a+b*arctanh(c*x))^2+-1//10*b^2*c^3*d^3*x^-3+-1//60*b^2*c^2*d^3*x^-4+-1//120*b^2*c^6*d^3*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+14//15*b^2*c^6*d^3*Polylogarithms.polylog(2,c*x)+37//30*b^2*c^6*d^3*arctanh(c*x)+37//40*b^2*c^6*d^3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+113//45*b^2*c^6*d^3*log(x)+-14//15*b*c^4*d^3*x^-2*(a+b*arctanh(c*x))+-11//6*b*c^5*d^3*x^-1*(a+b*arctanh(c*x))+-11//18*b*c^3*d^3*x^-3*(a+b*arctanh(c*x))+-3//10*b*c^2*d^3*x^-4*(a+b*arctanh(c*x))+-1//15*b*c*d^3*x^-5*(a+b*arctanh(c*x))+1//60*b*c^6*d^3*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+28//15*a*b*c^6*d^3*log(x)+37//20*b*c^6*d^3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x^3*(a+b*arctanh(c*x))^2*(d+c*d*x)^-1, x) == :(11//6*c^-4*d^-1*(a+b*arctanh(c*x))^2+x*c^-3*d^-1*(a+b*arctanh(c*x))^2+c^-4*d^-1*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-4//3*b^2*c^-4*d^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//2*b^2*c^-4*d^-1*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1//2*b^2*c^-4*d^-1*log(1+-1*c^2*x^2)+-1//2*c^-2*d^-1*x^2*(a+b*arctanh(c*x))^2+-1//3*b^2*c^-4*d^-1*arctanh(c*x)+1//3*x*b^2*c^-3*d^-1+1//3*c^-1*d^-1*x^3*(a+b*arctanh(c*x))^2+-1*a*b*x*c^-3*d^-1+-1*b*c^-4*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*x*b^2*c^-3*d^-1*arctanh(c*x)+-8//3*b*c^-4*d^-1*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//3*b*c^-2*d^-1*x^2*(a+b*arctanh(c*x)))
@test integrate(x^2*(a+b*arctanh(c*x))^2*(d+c*d*x)^-1, x) == :(-3//2*c^-3*d^-1*(a+b*arctanh(c*x))^2+b^2*c^-3*d^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+(1/2)*b^2*c^-3*d^-1*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+(1/2)*b^2*c^-3*d^-1*log(1+-1*c^2*x^2)+(1/2)*c^-1*d^-1*x^2*(a+b*arctanh(c*x))^2+-1*x*c^-2*d^-1*(a+b*arctanh(c*x))^2+-1*c^-3*d^-1*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+a*b*x*c^-2*d^-1+b*c^-3*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+x*b^2*c^-2*d^-1*arctanh(c*x)+2*b*c^-3*d^-1*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x*(a+b*arctanh(c*x))^2*(d+c*d*x)^-1, x) == :(c^-2*d^-1*(a+b*arctanh(c*x))^2+x*c^-1*d^-1*(a+b*arctanh(c*x))^2+c^-2*d^-1*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-1*b^2*c^-2*d^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//2*b^2*c^-2*d^-1*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1*b*c^-2*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-2*b*c^-2*d^-1*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate((a+b*arctanh(c*x))^2*(d+c*d*x)^-1, x) == :((1/2)*b^2*c^-1*d^-1*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1*c^-1*d^-1*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+b*c^-1*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x))^2*(d+c*d*x)^-1, x) == :(d^-1*(a+b*arctanh(c*x))^2*log(2+-2*(1+c*x)^-1)+-1//2*b^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+c*x)^-1)+-1*b*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1))
@test integrate(x^-2*(a+b*arctanh(c*x))^2*(d+c*d*x)^-1, x) == :(c*d^-1*(a+b*arctanh(c*x))^2+-1*d^-1*x^-1*(a+b*arctanh(c*x))^2+(1/2)*c*b^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+c*x)^-1)+-1*c*b^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1*c*d^-1*(a+b*arctanh(c*x))^2*log(2+-2*(1+c*x)^-1)+b*c*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+2*b*c*d^-1*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x))^2*(d+c*d*x)^-1, x) == :(-1//2*c^2*d^-1*(a+b*arctanh(c*x))^2+-1//2*d^-1*x^-2*(a+b*arctanh(c*x))^2+c*d^-1*x^-1*(a+b*arctanh(c*x))^2+b^2*c^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+b^2*c^2*d^-1*log(x)+c^2*d^-1*(a+b*arctanh(c*x))^2*log(2+-2*(1+c*x)^-1)+-1//2*b^2*c^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+c*x)^-1)+-1//2*b^2*c^2*d^-1*log(1+-1*c^2*x^2)+-1*b*c*d^-1*x^-1*(a+b*arctanh(c*x))+-1*b*c^2*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-2*b*c^2*d^-1*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-4*(a+b*arctanh(c*x))^2*(d+c*d*x)^-1, x) == :(-1//3*d^-1*x^-3*(a+b*arctanh(c*x))^2+5//6*c^3*d^-1*(a+b*arctanh(c*x))^2+(1/2)*c*d^-1*x^-2*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^3*d^-1*Polylogarithms.polylog(3,-1+2*(1+c*x)^-1)+(1/2)*b^2*c^3*d^-1*log(1+-1*c^2*x^2)+-1*b^2*c^3*d^-1*log(x)+-1*c^2*d^-1*x^-1*(a+b*arctanh(c*x))^2+-1*c^3*d^-1*(a+b*arctanh(c*x))^2*log(2+-2*(1+c*x)^-1)+-4//3*b^2*c^3*d^-1*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1//3*b^2*c^2*d^-1*x^-1+1//3*b^2*c^3*d^-1*arctanh(c*x)+b*c^2*d^-1*x^-1*(a+b*arctanh(c*x))+b*c^3*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1//3*b*c*d^-1*x^-2*(a+b*arctanh(c*x))+8//3*b*c^3*d^-1*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^4*(a+b*arctanh(c*x))^2*(d+c*d*x)^-2, x) == :(29//6*c^-5*d^-2*(a+b*arctanh(c*x))^2+-1*b^2*c^-5*d^-2*log(1+-1*c^2*x^2)+-1*c^-5*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))^2+-1*c^-3*d^-2*x^2*(a+b*arctanh(c*x))^2+-2*b^2*c^-5*d^-2*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+3*x*c^-4*d^-2*(a+b*arctanh(c*x))^2+4*c^-5*d^-2*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-10//3*b^2*c^-5*d^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//2*b^2*c^-5*d^-2*(1+c*x)^-1+1//3*x*b^2*c^-4*d^-2+1//3*c^-2*d^-2*x^3*(a+b*arctanh(c*x))^2+1//6*b^2*c^-5*d^-2*arctanh(c*x)+-1*b*c^-5*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+-4*b*c^-5*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-2*a*b*x*c^-4*d^-2+-2*x*b^2*c^-4*d^-2*arctanh(c*x)+-20//3*b*c^-5*d^-2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//3*b*c^-3*d^-2*x^2*(a+b*arctanh(c*x)))
@test integrate(x^3*(a+b*arctanh(c*x))^2*(d+c*d*x)^-2, x) == :(-3*c^-4*d^-2*(a+b*arctanh(c*x))^2+c^-4*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^-4*d^-2*(1+c*x)^-1+(1/2)*b^2*c^-4*d^-2*log(1+-1*c^2*x^2)+(1/2)*c^-2*d^-2*x^2*(a+b*arctanh(c*x))^2+-3*c^-4*d^-2*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-2*x*c^-3*d^-2*(a+b*arctanh(c*x))^2+2*b^2*c^-4*d^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//2*b^2*c^-4*d^-2*arctanh(c*x)+3//2*b^2*c^-4*d^-2*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+a*b*x*c^-3*d^-2+b*c^-4*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+x*b^2*c^-3*d^-2*arctanh(c*x)+3*b*c^-4*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+4*b*c^-4*d^-2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x^2*(a+b*arctanh(c*x))^2*(d+c*d*x)^-2, x) == :(3//2*c^-3*d^-2*(a+b*arctanh(c*x))^2+x*c^-2*d^-2*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^-3*d^-2*arctanh(c*x)+-1*b^2*c^-3*d^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1*b^2*c^-3*d^-2*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1*c^-3*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))^2+2*c^-3*d^-2*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-1//2*b^2*c^-3*d^-2*(1+c*x)^-1+-1*b*c^-3*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+-2*b*c^-3*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-2*b*c^-3*d^-2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x*(a+b*arctanh(c*x))^2*(d+c*d*x)^-2, x) == :(-1//2*c^-2*d^-2*(a+b*arctanh(c*x))^2+c^-2*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^-2*d^-2*(1+c*x)^-1+(1/2)*b^2*c^-2*d^-2*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1*c^-2*d^-2*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-1//2*b^2*c^-2*d^-2*arctanh(c*x)+b*c^-2*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+b*c^-2*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1))
@test integrate((a+b*arctanh(c*x))^2*(d+c*d*x)^-2, x) == :((1/2)*c^-1*d^-2*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^-1*d^-2*arctanh(c*x)+-1*c^-1*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))^2+-1//2*b^2*c^-1*d^-2*(1+c*x)^-1+-1*b*c^-1*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x)))
@test integrate(x^-1*(a+b*arctanh(c*x))^2*(d+c*d*x)^-2, x) == :(-1//2*d^-2*(a+b*arctanh(c*x))^2+d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))^2+d^-2*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+(1/2)*b^2*d^-2*(1+c*x)^-1+(1/2)*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+2*d^-2*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-1//2*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1//2*b^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+-1//2*b^2*d^-2*arctanh(c*x)+b*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+b*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+-1*b*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*b*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1))
@test integrate(x^-2*(a+b*arctanh(c*x))^2*(d+c*d*x)^-2, x) == :(-1*d^-2*x^-1*(a+b*arctanh(c*x))^2+3//2*c*d^-2*(a+b*arctanh(c*x))^2+c*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+c*b^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+(1/2)*c*b^2*d^-2*arctanh(c*x)+-1*c*b^2*d^-2*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1*c*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-1*c*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))^2+-4*c*d^-2*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-2*c*d^-2*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-1//2*c*b^2*d^-2*(1+c*x)^-1+-1*b*c*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+-2*b*c*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+2*b*c*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+2*b*c*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+2*b*c*d^-2*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x))^2*(d+c*d*x)^-2, x) == :(-2*c^2*d^-2*(a+b*arctanh(c*x))^2+-1//2*d^-2*x^-2*(a+b*arctanh(c*x))^2+b^2*c^2*d^-2*log(x)+c^2*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^2*d^-2*(1+c*x)^-1+2*c*d^-2*x^-1*(a+b*arctanh(c*x))^2+2*b^2*c^2*d^-2*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+3*c^2*d^-2*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+6*c^2*d^-2*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-3//2*b^2*c^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-3//2*b^2*c^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+-1//2*b^2*c^2*d^-2*arctanh(c*x)+-1//2*b^2*c^2*d^-2*log(1+-1*c^2*x^2)+3//2*b^2*c^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+b*c^2*d^-2*(1+c*x)^-1*(a+b*arctanh(c*x))+-1*b*c*d^-2*x^-1*(a+b*arctanh(c*x))+-4*b*c^2*d^-2*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1)+-3*b*c^2*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-3*b*c^2*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+3*b*c^2*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1))
@test integrate(x^4*(a+b*arctanh(c*x))^2*(d+c*d*x)^-3, x) == :(-43//8*c^-5*d^-3*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^-5*d^-3*log(1+-1*c^2*x^2)+(1/2)*c^-3*d^-3*x^2*(a+b*arctanh(c*x))^2+-6*c^-5*d^-3*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-3*x*c^-4*d^-3*(a+b*arctanh(c*x))^2+3*b^2*c^-5*d^-3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+3*b^2*c^-5*d^-3*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+4*c^-5*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))^2+-29//16*b^2*c^-5*d^-3*arctanh(c*x)+-1//2*c^-5*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))^2+-1//16*b^2*c^-5*d^-3*(1+c*x)^-2+29//16*b^2*c^-5*d^-3*(1+c*x)^-1+a*b*x*c^-4*d^-3+x*b^2*c^-4*d^-3*arctanh(c*x)+6*b*c^-5*d^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+6*b*c^-5*d^-3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+-1//4*b*c^-5*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+15//4*b*c^-5*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x)))
@test integrate(x^3*(a+b*arctanh(c*x))^2*(d+c*d*x)^-3, x) == :(19//8*c^-4*d^-3*(a+b*arctanh(c*x))^2+x*c^-3*d^-3*(a+b*arctanh(c*x))^2+(1/2)*c^-4*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))^2+-1*b^2*c^-4*d^-3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-3*c^-4*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))^2+3*c^-4*d^-3*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-21//16*b^2*c^-4*d^-3*(1+c*x)^-1+-3//2*b^2*c^-4*d^-3*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+1//16*b^2*c^-4*d^-3*(1+c*x)^-2+21//16*b^2*c^-4*d^-3*arctanh(c*x)+-3*b*c^-4*d^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-2*b*c^-4*d^-3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+-11//4*b*c^-4*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))+1//4*b*c^-4*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x)))
@test integrate(x^2*(a+b*arctanh(c*x))^2*(d+c*d*x)^-3, x) == :(-7//8*c^-3*d^-3*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^-3*d^-3*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1*c^-3*d^-3*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+2*c^-3*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))^2+-13//16*b^2*c^-3*d^-3*arctanh(c*x)+-1//2*c^-3*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))^2+-1//16*b^2*c^-3*d^-3*(1+c*x)^-2+13//16*b^2*c^-3*d^-3*(1+c*x)^-1+b*c^-3*d^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1//4*b*c^-3*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+7//4*b*c^-3*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x)))
@test integrate(x*(a+b*arctanh(c*x))^2*(d+c*d*x)^-3, x) == :(-1//8*c^-2*d^-3*(a+b*arctanh(c*x))^2+(1/2)*d^-3*x^2*(1+c*x)^-2*(a+b*arctanh(c*x))^2+-5//16*b^2*c^-2*d^-3*(1+c*x)^-1+1//16*b^2*c^-2*d^-3*(1+c*x)^-2+5//16*b^2*c^-2*d^-3*arctanh(c*x)+-3//4*b*c^-2*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))+1//4*b*c^-2*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x)))
@test integrate((a+b*arctanh(c*x))^2*(d+c*d*x)^-3, x) == :(1//8*c^-1*d^-3*(a+b*arctanh(c*x))^2+-3//16*b^2*c^-1*d^-3*(1+c*x)^-1+-1//2*c^-1*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))^2+-1//16*b^2*c^-1*d^-3*(1+c*x)^-2+3//16*b^2*c^-1*d^-3*arctanh(c*x)+-1//4*b*c^-1*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))+-1//4*b*c^-1*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x)))
@test integrate(x^-1*(a+b*arctanh(c*x))^2*(d+c*d*x)^-3, x) == :(-5//8*d^-3*(a+b*arctanh(c*x))^2+d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))^2+d^-3*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+(1/2)*b^2*d^-3*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+(1/2)*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))^2+2*d^-3*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-11//16*b^2*d^-3*arctanh(c*x)+-1//2*b^2*d^-3*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1//2*b^2*d^-3*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+1//16*b^2*d^-3*(1+c*x)^-2+11//16*b^2*d^-3*(1+c*x)^-1+b*d^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+-1*b*d^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*b*d^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//4*b*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))+5//4*b*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x)))
@test integrate(x^-2*(a+b*arctanh(c*x))^2*(d+c*d*x)^-3, x) == :(-1*d^-3*x^-1*(a+b*arctanh(c*x))^2+17//8*c*d^-3*(a+b*arctanh(c*x))^2+-1*c*b^2*d^-3*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-6*c*d^-3*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-3*c*d^-3*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-2*c*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))^2+-19//16*c*b^2*d^-3*(1+c*x)^-1+-3//2*c*b^2*d^-3*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-1//2*c*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x))^2+-1//16*c*b^2*d^-3*(1+c*x)^-2+3//2*c*b^2*d^-3*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+3//2*c*b^2*d^-3*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+19//16*c*b^2*d^-3*arctanh(c*x)+-3*b*c*d^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+2*b*c*d^-3*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1)+3*b*c*d^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+3*b*c*d^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-9//4*b*c*d^-3*(1+c*x)^-1*(a+b*arctanh(c*x))+-1//4*b*c*d^-3*(1+c*x)^-2*(a+b*arctanh(c*x)))
@test integrate((1+c*x)^-4*(a+b*arctanh(c*x))^2, x) == :(1//24*c^-1*(a+b*arctanh(c*x))^2+-11//144*b^2*c^-1*(1+c*x)^-1+-5//144*b^2*c^-1*(1+c*x)^-2+-1//3*c^-1*(1+c*x)^-3*(a+b*arctanh(c*x))^2+-1//54*b^2*c^-1*(1+c*x)^-3+11//144*b^2*c^-1*arctanh(c*x)+-1//9*b*c^-1*(1+c*x)^-3*(a+b*arctanh(c*x))+-1//12*b*c^-1*(1+c*x)^-1*(a+b*arctanh(c*x))+-1//12*b*c^-1*(1+c*x)^-2*(a+b*arctanh(c*x)))
@test integrate((c*x+-1*a*c*x^2)^-1*arctanh(a*x)^2, x) == :(-1//2*c^-1*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+c^-1*arctanh(a*x)^2*log(2+-2*(1+-1*a*x)^-1)+c^-1*Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)*arctanh(a*x))
@test integrate((1+c*x)^3*(a+b*arctanh(c*x))^3, x) == :(1//4*x*b^3+3*a*x*b^2+3*x*b^3*arctanh(c*x)+3*b^3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+4*b*c^-1*(a+b*arctanh(c*x))^2+-11//2*b^3*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//4*b^3*c^-1*arctanh(c*x)+1//4*c^-1*(1+c*x)^4*(a+b*arctanh(c*x))^3+3//2*b^3*c^-1*log(1+-1*c^2*x^2)+21//4*b*x*(a+b*arctanh(c*x))^2+-11*b^2*c^-1*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+-6*b*c^-1*(a+b*arctanh(c*x))^2*log(2*(1+-1*c*x)^-1)+-6*b^2*c^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//4*b*c^2*x^3*(a+b*arctanh(c*x))^2+1//4*c*b^2*x^2*(a+b*arctanh(c*x))+3//2*b*c*x^2*(a+b*arctanh(c*x))^2)
@test integrate((1+c*x)^2*(a+b*arctanh(c*x))^3, x) == :(a*x*b^2+x*b^3*arctanh(c*x)+(1/2)*b^3*c^-1*log(1+-1*c^2*x^2)+-3*b^3*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+2*b^3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+3*b*x*(a+b*arctanh(c*x))^2+1//3*c^-1*(1+c*x)^3*(a+b*arctanh(c*x))^3+5//2*b*c^-1*(a+b*arctanh(c*x))^2+(1/2)*b*c*x^2*(a+b*arctanh(c*x))^2+-6*b^2*c^-1*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+-4*b*c^-1*(a+b*arctanh(c*x))^2*log(2*(1+-1*c*x)^-1)+-4*b^2*c^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1))
@test integrate((a+b*arctanh(c*x))^3*(1+c*x), x) == :((1/2)*c^-1*(1+c*x)^2*(a+b*arctanh(c*x))^3+-3//2*b^3*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+3//2*b*x*(a+b*arctanh(c*x))^2+3//2*b*c^-1*(a+b*arctanh(c*x))^2+3//2*b^3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-3*b*c^-1*(a+b*arctanh(c*x))^2*log(2*(1+-1*c*x)^-1)+-3*b^2*c^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-3*b^2*c^-1*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate((1+c*x)^-1*(a+b*arctanh(c*x))^3, x) == :(-1*c^-1*(a+b*arctanh(c*x))^3*log(2*(1+c*x)^-1)+3//4*b^3*c^-1*Polylogarithms.polylog(4,1+-2*(1+c*x)^-1)+3//2*b*c^-1*(a+b*arctanh(c*x))^2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+3//2*b^2*c^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1))
@test integrate((1+c*x)^-2*(a+b*arctanh(c*x))^3, x) == :((1/2)*c^-1*(a+b*arctanh(c*x))^3+-1*c^-1*(1+c*x)^-1*(a+b*arctanh(c*x))^3+-3//4*b^3*c^-1*(1+c*x)^-1+3//4*b*c^-1*(a+b*arctanh(c*x))^2+3//4*b^3*c^-1*arctanh(c*x)+-3//2*b*c^-1*(1+c*x)^-1*(a+b*arctanh(c*x))^2+-3//2*b^2*c^-1*(1+c*x)^-1*(a+b*arctanh(c*x)))
@test integrate((1+c*x)^-3*(a+b*arctanh(c*x))^3, x) == :(1//8*c^-1*(a+b*arctanh(c*x))^3+-21//64*b^3*c^-1*(1+c*x)^-1+-3//64*b^3*c^-1*(1+c*x)^-2+-1//2*c^-1*(1+c*x)^-2*(a+b*arctanh(c*x))^3+9//32*b*c^-1*(a+b*arctanh(c*x))^2+21//64*b^3*c^-1*arctanh(c*x)+-9//16*b^2*c^-1*(1+c*x)^-1*(a+b*arctanh(c*x))+-3//8*b*c^-1*(1+c*x)^-1*(a+b*arctanh(c*x))^2+-3//8*b*c^-1*(1+c*x)^-2*(a+b*arctanh(c*x))^2+-3//16*b^2*c^-1*(1+c*x)^-2*(a+b*arctanh(c*x)))
@test integrate((1+c*x)^-4*(a+b*arctanh(c*x))^3, x) == :(1//24*c^-1*(a+b*arctanh(c*x))^3+-85//576*b^3*c^-1*(1+c*x)^-1+-19//576*b^3*c^-1*(1+c*x)^-2+-1//3*c^-1*(1+c*x)^-3*(a+b*arctanh(c*x))^3+-1//108*b^3*c^-1*(1+c*x)^-3+11//96*b*c^-1*(a+b*arctanh(c*x))^2+85//576*b^3*c^-1*arctanh(c*x)+-11//48*b^2*c^-1*(1+c*x)^-1*(a+b*arctanh(c*x))+-5//48*b^2*c^-1*(1+c*x)^-2*(a+b*arctanh(c*x))+-1//6*b*c^-1*(1+c*x)^-3*(a+b*arctanh(c*x))^2+-1//8*b*c^-1*(1+c*x)^-1*(a+b*arctanh(c*x))^2+-1//8*b*c^-1*(1+c*x)^-2*(a+b*arctanh(c*x))^2+-1//18*b^2*c^-1*(1+c*x)^-3*(a+b*arctanh(c*x)))
@test integrate(x^2*(c+a*c*x)^-1*arctanh(a*x)^3, x) == :(-3//2*a^-3*c^-1*arctanh(a*x)^3+-3//2*a^-3*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-3//2*a^-3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+3//2*a^-3*c^-1*arctanh(a*x)^2+3//4*a^-3*c^-1*Polylogarithms.polylog(4,1+-2*(1+a*x)^-1)+(1/2)*a^-1*c^-1*x^2*arctanh(a*x)^3+-1*x*a^-2*c^-1*arctanh(a*x)^3+-1*a^-3*c^-1*arctanh(a*x)^3*log(2*(1+a*x)^-1)+-3*a^-3*c^-1*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+3*a^-3*c^-1*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+3*a^-3*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+3//2*x*a^-2*c^-1*arctanh(a*x)^2+3//2*a^-3*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+a*x)^-1)+3//2*a^-3*c^-1*Polylogarithms.polylog(3,1+-2*(1+a*x)^-1)*arctanh(a*x))
@test integrate(x*(c+a*c*x)^-1*arctanh(a*x)^3, x) == :(a^-2*c^-1*arctanh(a*x)^3+-3//4*a^-2*c^-1*Polylogarithms.polylog(4,1+-2*(1+a*x)^-1)+3//2*a^-2*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+x*a^-1*c^-1*arctanh(a*x)^3+a^-2*c^-1*arctanh(a*x)^3*log(2*(1+a*x)^-1)+-3*a^-2*c^-1*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+-3*a^-2*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-3//2*a^-2*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+a*x)^-1)+-3//2*a^-2*c^-1*Polylogarithms.polylog(3,1+-2*(1+a*x)^-1)*arctanh(a*x))
@test integrate((c+a*c*x)^-1*arctanh(a*x)^3, x) == :(3//4*a^-1*c^-1*Polylogarithms.polylog(4,1+-2*(1+a*x)^-1)+-1*a^-1*c^-1*arctanh(a*x)^3*log(2*(1+a*x)^-1)+3//2*a^-1*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+a*x)^-1)+3//2*a^-1*c^-1*Polylogarithms.polylog(3,1+-2*(1+a*x)^-1)*arctanh(a*x))
@test integrate(x^-1*(c+a*c*x)^-1*arctanh(a*x)^3, x) == :(-3//4*c^-1*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+c^-1*arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+-3//2*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//2*c^-1*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x))
@test integrate((c*x+a*c*x^2)^-1*arctanh(a*x)^3, x) == :(-3//4*c^-1*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+c^-1*arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+-3//2*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//2*c^-1*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x))
@test integrate(x^-2*(c+a*c*x)^-1*arctanh(a*x)^3, x) == :(a*c^-1*arctanh(a*x)^3+-1*c^-1*x^-1*arctanh(a*x)^3+-3//2*a*c^-1*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+3//4*a*c^-1*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+-1*a*c^-1*arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+-3*a*c^-1*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x)+3*a*c^-1*arctanh(a*x)^2*log(2+-2*(1+a*x)^-1)+3//2*a*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+3//2*a*c^-1*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x))
@test integrate(x^-3*(c+a*c*x)^-1*arctanh(a*x)^3, x) == :(-3//2*a^2*c^-1*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//4*a^2*c^-1*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+-1//2*a^2*c^-1*arctanh(a*x)^3+-1//2*c^-1*x^-2*arctanh(a*x)^3+3//2*a^2*c^-1*arctanh(a*x)^2+3//2*a^2*c^-1*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+a*c^-1*x^-1*arctanh(a*x)^3+a^2*c^-1*arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+-3*a^2*c^-1*arctanh(a*x)^2*log(2+-2*(1+a*x)^-1)+3*a^2*c^-1*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x)+3*a^2*c^-1*arctanh(a*x)*log(2+-2*(1+a*x)^-1)+-3//2*a*c^-1*x^-1*arctanh(a*x)^2+-3//2*a^2*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//2*a^2*c^-1*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x))
@test integrate(x^2*(c+-1*a*c*x)^-1*arctanh(a*x)^4, x) == :(-3*a^-3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-2*a^-3*c^-1*arctanh(a*x)^3+3*a^-3*c^-1*Polylogarithms.polylog(4,1+-2*(1+-1*a*x)^-1)+-3//2*a^-3*c^-1*Polylogarithms.polylog(5,1+-2*(1+-1*a*x)^-1)+-1//2*a^-3*c^-1*arctanh(a*x)^4+a^-3*c^-1*arctanh(a*x)^4*log(2*(1+-1*a*x)^-1)+-1*x*a^-2*c^-1*arctanh(a*x)^4+-6*a^-3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-3*a^-3*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-2*x*a^-2*c^-1*arctanh(a*x)^3+2*a^-3*c^-1*arctanh(a*x)^3*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+3*a^-3*c^-1*Polylogarithms.polylog(4,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+4*a^-3*c^-1*arctanh(a*x)^3*log(2*(1+-1*a*x)^-1)+6*a^-3*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+6*a^-3*c^-1*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+6*a^-3*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-1//2*a^-1*c^-1*x^2*arctanh(a*x)^4)
@test integrate(x*(c+-1*a*c*x)^-1*arctanh(a*x)^4, x) == :(-1*a^-2*c^-1*arctanh(a*x)^4+3*a^-2*c^-1*Polylogarithms.polylog(4,1+-2*(1+-1*a*x)^-1)+-3//2*a^-2*c^-1*Polylogarithms.polylog(5,1+-2*(1+-1*a*x)^-1)+a^-2*c^-1*arctanh(a*x)^4*log(2*(1+-1*a*x)^-1)+-1*x*a^-1*c^-1*arctanh(a*x)^4+-6*a^-2*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-3*a^-2*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+2*a^-2*c^-1*arctanh(a*x)^3*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+3*a^-2*c^-1*Polylogarithms.polylog(4,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+4*a^-2*c^-1*arctanh(a*x)^3*log(2*(1+-1*a*x)^-1)+6*a^-2*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1))
@test integrate((c+-1*a*c*x)^-1*arctanh(a*x)^4, x) == :(-3//2*a^-1*c^-1*Polylogarithms.polylog(5,1+-2*(1+-1*a*x)^-1)+a^-1*c^-1*arctanh(a*x)^4*log(2*(1+-1*a*x)^-1)+-3*a^-1*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+2*a^-1*c^-1*arctanh(a*x)^3*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+3*a^-1*c^-1*Polylogarithms.polylog(4,1+-2*(1+-1*a*x)^-1)*arctanh(a*x))
@test integrate(x^-1*(c+-1*a*c*x)^-1*arctanh(a*x)^4, x) == :(-3//2*c^-1*Polylogarithms.polylog(5,-1+2*(1+-1*a*x)^-1)+c^-1*arctanh(a*x)^4*log(2+-2*(1+-1*a*x)^-1)+-3*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+2*c^-1*arctanh(a*x)^3*Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)+3*c^-1*Polylogarithms.polylog(4,-1+2*(1+-1*a*x)^-1)*arctanh(a*x))
@test integrate((c*x+-1*a*c*x^2)^-1*arctanh(a*x)^4, x) == :(-3//2*c^-1*Polylogarithms.polylog(5,-1+2*(1+-1*a*x)^-1)+c^-1*arctanh(a*x)^4*log(2+-2*(1+-1*a*x)^-1)+-3*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+2*c^-1*arctanh(a*x)^3*Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)+3*c^-1*Polylogarithms.polylog(4,-1+2*(1+-1*a*x)^-1)*arctanh(a*x))
@test integrate(x^-2*(c+-1*a*c*x)^-1*arctanh(a*x)^4, x) == :(a*c^-1*arctanh(a*x)^4+-1*c^-1*x^-1*arctanh(a*x)^4+-3*a*c^-1*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+-3//2*a*c^-1*Polylogarithms.polylog(5,-1+2*(1+-1*a*x)^-1)+a*c^-1*arctanh(a*x)^4*log(2+-2*(1+-1*a*x)^-1)+-6*a*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-6*a*c^-1*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x)+-3*a*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+2*a*c^-1*arctanh(a*x)^3*Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)+3*a*c^-1*Polylogarithms.polylog(4,-1+2*(1+-1*a*x)^-1)*arctanh(a*x)+4*a*c^-1*arctanh(a*x)^3*log(2+-2*(1+a*x)^-1))
@test integrate(x^-3*(c+-1*a*c*x)^-1*arctanh(a*x)^4, x) == :(-3*a^2*c^-1*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+-3*a^2*c^-1*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+2*a^2*c^-1*arctanh(a*x)^3+-3//2*a^2*c^-1*Polylogarithms.polylog(5,-1+2*(1+-1*a*x)^-1)+-1//2*c^-1*x^-2*arctanh(a*x)^4+3//2*a^2*c^-1*arctanh(a*x)^4+a^2*c^-1*arctanh(a*x)^4*log(2+-2*(1+-1*a*x)^-1)+-1*a*c^-1*x^-1*arctanh(a*x)^4+-6*a^2*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-6*a^2*c^-1*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x)+-6*a^2*c^-1*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x)+-3*a^2*c^-1*arctanh(a*x)^2*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+-2*a*c^-1*x^-1*arctanh(a*x)^3+2*a^2*c^-1*arctanh(a*x)^3*Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)+3*a^2*c^-1*Polylogarithms.polylog(4,-1+2*(1+-1*a*x)^-1)*arctanh(a*x)+4*a^2*c^-1*arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+6*a^2*c^-1*arctanh(a*x)^2*log(2+-2*(1+a*x)^-1))
@test integrate(x^3*(d+e*x)^-1*(a+b*arctanh(c*x)), x) == :(1//3*e^-1*x^3*(a+b*arctanh(c*x))+a*x*d^2*e^-3+d^3*e^-4*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*d^3*e^-4*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*d^3*e^-4*(a+b*arctanh(c*x))*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1//2*b*d^3*e^-4*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1//2*d*e^-2*x^2*(a+b*arctanh(c*x))+1//6*b*c^-1*e^-1*x^2+1//6*b*c^-3*e^-1*log(1+-1*c^2*x^2)+b*x*d^2*e^-3*arctanh(c*x)+(1/2)*b*d*c^-2*e^-2*arctanh(c*x)+(1/2)*b*c^-1*d^2*e^-3*log(1+-1*c^2*x^2)+-1//2*b*d*x*c^-1*e^-2)
@test integrate(x^2*(d+e*x)^-1*(a+b*arctanh(c*x)), x) == :((1/2)*e^-1*x^2*(a+b*arctanh(c*x))+d^2*e^-3*(a+b*arctanh(c*x))*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+(1/2)*b*x*c^-1*e^-1+(1/2)*b*d^2*e^-3*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*a*d*x*e^-2+-1*d^2*e^-3*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-1//2*b*c^-2*e^-1*arctanh(c*x)+-1//2*b*d^2*e^-3*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*b*d*x*e^-2*arctanh(c*x)+-1//2*b*d*c^-1*e^-2*log(1+-1*c^2*x^2))
@test integrate(x*(d+e*x)^-1*(a+b*arctanh(c*x)), x) == :(a*x*e^-1+b*x*e^-1*arctanh(c*x)+d*e^-2*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*d*e^-2*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+(1/2)*b*c^-1*e^-1*log(1+-1*c^2*x^2)+-1*d*e^-2*(a+b*arctanh(c*x))*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1//2*b*d*e^-2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1))
@test integrate((d+e*x)^-1*(a+b*arctanh(c*x)), x) == :(e^-1*(a+b*arctanh(c*x))*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+(1/2)*b*e^-1*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*e^-1*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-1//2*b*e^-1*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x)))
@test integrate(x^-1*(d+e*x)^-1*(a+b*arctanh(c*x)), x) == :(a*d^-1*log(x)+d^-1*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*d^-1*Polylogarithms.polylog(2,c*x)+(1/2)*b*d^-1*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*d^-1*(a+b*arctanh(c*x))*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1//2*b*d^-1*Polylogarithms.polylog(2,-1*c*x)+-1//2*b*d^-1*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1))
@test integrate(x^-2*(d+e*x)^-1*(a+b*arctanh(c*x)), x) == :(-1*d^-1*x^-1*(a+b*arctanh(c*x))+b*c*d^-1*log(x)+e*d^-2*(a+b*arctanh(c*x))*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+(1/2)*b*e*d^-2*Polylogarithms.polylog(2,-1*c*x)+(1/2)*b*e*d^-2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*a*e*d^-2*log(x)+-1*e*d^-2*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+-1//2*b*c*d^-1*log(1+-1*c^2*x^2)+-1//2*b*e*d^-2*Polylogarithms.polylog(2,c*x)+-1//2*b*e*d^-2*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x)))
@test integrate(x^-3*(d+e*x)^-1*(a+b*arctanh(c*x)), x) == :(-1//2*d^-1*x^-2*(a+b*arctanh(c*x))+a*d^-3*e^2*log(x)+e*d^-2*x^-1*(a+b*arctanh(c*x))+d^-3*e^2*(a+b*arctanh(c*x))*log(2*(1+c*x)^-1)+(1/2)*b*c^2*d^-1*arctanh(c*x)+(1/2)*b*d^-3*e^2*Polylogarithms.polylog(2,c*x)+(1/2)*b*d^-3*e^2*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*d^-3*e^2*(a+b*arctanh(c*x))*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1//2*b*c*d^-1*x^-1+-1//2*b*d^-3*e^2*Polylogarithms.polylog(2,-1*c*x)+-1//2*b*d^-3*e^2*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+(1/2)*b*c*e*d^-2*log(1+-1*c^2*x^2)+-1*b*c*e*d^-2*log(x))
@test integrate(x^2*(a+b*arctanh(c*x))^2*(d+e*x)^-1, x) == :((1/2)*e^-1*x^2*(a+b*arctanh(c*x))^2+-1//2*c^-2*e^-1*(a+b*arctanh(c*x))^2+d^2*e^-3*(a+b*arctanh(c*x))^2*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+(1/2)*b^2*c^-2*e^-1*log(1+-1*c^2*x^2)+(1/2)*b^2*d^2*e^-3*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1*d*x*e^-2*(a+b*arctanh(c*x))^2+-1*d*c^-1*e^-2*(a+b*arctanh(c*x))^2+-1*d^2*e^-3*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-1//2*b^2*d^2*e^-3*Polylogarithms.polylog(3,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+a*b*x*c^-1*e^-1+b*d^2*e^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+d*b^2*c^-1*e^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+x*b^2*c^-1*e^-1*arctanh(c*x)+-1*b*d^2*e^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+2*b*d*c^-1*e^-2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x*(a+b*arctanh(c*x))^2*(d+e*x)^-1, x) == :(x*e^-1*(a+b*arctanh(c*x))^2+c^-1*e^-1*(a+b*arctanh(c*x))^2+d*e^-2*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+(1/2)*d*b^2*e^-2*Polylogarithms.polylog(3,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*d*e^-2*(a+b*arctanh(c*x))^2*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*b^2*c^-1*e^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//2*d*b^2*e^-2*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+b*d*e^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*b*d*e^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-2*b*c^-1*e^-1*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate((a+b*arctanh(c*x))^2*(d+e*x)^-1, x) == :(e^-1*(a+b*arctanh(c*x))^2*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+(1/2)*b^2*e^-1*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1*e^-1*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-1//2*b^2*e^-1*Polylogarithms.polylog(3,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+b*e^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*b*e^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x)))
@test integrate(x^-1*(a+b*arctanh(c*x))^2*(d+e*x)^-1, x) == :(d^-1*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+(1/2)*b^2*d^-1*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+(1/2)*b^2*d^-1*Polylogarithms.polylog(3,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*d^-1*(a+b*arctanh(c*x))^2*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+2*d^-1*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-1//2*b^2*d^-1*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1//2*b^2*d^-1*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+b*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+b*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+-1*b*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1*b*d^-1*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1))
@test integrate(x^-2*(a+b*arctanh(c*x))^2*(d+e*x)^-1, x) == :(c*d^-1*(a+b*arctanh(c*x))^2+-1*d^-1*x^-1*(a+b*arctanh(c*x))^2+e*d^-2*(a+b*arctanh(c*x))^2*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+(1/2)*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+(1/2)*e*b^2*d^-2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+-1*c*b^2*d^-1*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1*e*d^-2*(a+b*arctanh(c*x))^2*log(2*(1+c*x)^-1)+-2*e*d^-2*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-1//2*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-1//2*e*b^2*d^-2*Polylogarithms.polylog(3,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+b*e*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+b*e*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1*b*e*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*b*e*d^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+2*b*c*d^-1*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-1*(d+e*x)^-1*arctanh(c*x)^2, x) == :((1/2)*d^-1*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+(1/2)*d^-1*Polylogarithms.polylog(3,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1//2*d^-1*Polylogarithms.polylog(3,1+-2*(1+c*x)^-1)+-1//2*d^-1*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+d^-1*arctanh(c*x)^2*log(2*(1+c*x)^-1)+d^-1*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))*arctanh(c*x)+d^-1*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)*arctanh(c*x)+-1*d^-1*arctanh(c*x)^2*log(2*c*(1+c*x)^-1*(e+c*d)^-1*(d+e*x))+-1*d^-1*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)*arctanh(c*x)+-1*d^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)*arctanh(c*x)+2*d^-1*arctanh(c*x)^2*arctanh(1+-2*(1+-1*c*x)^-1))
@test integrate(x^4*(1+-1*a^2*x^2)*arctanh(a*x), x) == :(-1//42*a*x^6+1//5*x^5*arctanh(a*x)+1//35*a^-5*log(1+-1*a^2*x^2)+1//35*a^-3*x^2+1//70*a^-1*x^4+-1//7*a^2*x^7*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)*arctanh(a*x), x) == :(-1//12*a^-4*arctanh(a*x)+-1//30*a*x^5+1//4*x^4*arctanh(a*x)+1//12*x*a^-3+1//36*a^-1*x^3+-1//6*a^2*x^6*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)*arctanh(a*x), x) == :(-1//20*a*x^4+1//3*x^3*arctanh(a*x)+1//15*a^-1*x^2+1//15*a^-3*log(1+-1*a^2*x^2)+-1//5*a^2*x^5*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)*arctanh(a*x), x) == :(-1//12*a*x^3+1//4*x*a^-1+-1//4*a^-2*(1+-1*a^2*x^2)^2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)*arctanh(a*x), x) == :(1//3*a^-1*log(1+-1*a^2*x^2)+1//6*a^-1*(1+-1*a^2*x^2)+2//3*x*arctanh(a*x)+1//3*x*(1+-1*a^2*x^2)*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)*arctanh(a*x), x) == :((1/2)*Polylogarithms.polylog(2,a*x)+(1/2)*arctanh(a*x)+-1//2*Polylogarithms.polylog(2,-1*a*x)+-1//2*a*x+-1//2*a^2*x^2*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)*arctanh(a*x), x) == :(a*log(x)+-1*a*log(1+-1*a^2*x^2)+-1*x^-1*arctanh(a*x)+-1*x*a^2*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)*arctanh(a*x), x) == :((1/2)*a^2*Polylogarithms.polylog(2,-1*a*x)+(1/2)*a^2*arctanh(a*x)+-1//2*a*x^-1+-1//2*a^2*Polylogarithms.polylog(2,a*x)+-1//2*x^-2*arctanh(a*x))
@test integrate(x^-4*(1+-1*a^2*x^2)*arctanh(a*x), x) == :(-2//3*a^3*log(x)+-1//3*x^-3*arctanh(a*x)+-1//6*a*x^-2+1//3*a^3*log(1+-1*a^2*x^2)+a^2*x^-1*arctanh(a*x))
@test integrate(x^-5*(1+-1*a^2*x^2)*arctanh(a*x), x) == :(-1//12*a*x^-3+1//4*a^3*x^-1+-1//4*x^-4*(1+-1*a^2*x^2)^2*arctanh(a*x))
@test integrate(x^-6*(1+-1*a^2*x^2)*arctanh(a*x), x) == :(-2//15*a^5*log(x)+-1//5*x^-5*arctanh(a*x)+-1//20*a*x^-4+1//15*a^3*x^-2+1//15*a^5*log(1+-1*a^2*x^2)+1//3*a^2*x^-3*arctanh(a*x))
@test integrate(x^4*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(-1//105*x^5+-4//105*a^-5*arctanh(a*x)+-2//35*a^-5*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-2//315*a^-2*x^3+1//5*x^5*arctanh(a*x)^2+2//35*a^-5*arctanh(a*x)^2+4//105*x*a^-4+-4//35*a^-5*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+-1//7*a^2*x^7*arctanh(a*x)^2+-1//21*a*x^6*arctanh(a*x)+1//35*a^-1*x^4*arctanh(a*x)+2//35*a^-3*x^2*arctanh(a*x))
@test integrate(x^3*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(-1//60*x^4+-1//12*a^-4*arctanh(a*x)^2+-1//180*a^-2*x^2+1//4*x^4*arctanh(a*x)^2+7//90*a^-4*log(1+-1*a^2*x^2)+-1//6*a^2*x^6*arctanh(a*x)^2+-1//15*a*x^5*arctanh(a*x)+1//6*x*a^-3*arctanh(a*x)+1//18*a^-1*x^3*arctanh(a*x))
@test integrate(x^2*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(-1//30*x^3+-2//15*a^-3*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-1//30*a^-3*arctanh(a*x)+1//3*x^3*arctanh(a*x)^2+1//30*x*a^-2+2//15*a^-3*arctanh(a*x)^2+-4//15*a^-3*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+-1//5*a^2*x^5*arctanh(a*x)^2+-1//10*a*x^4*arctanh(a*x)+2//15*a^-1*x^2*arctanh(a*x))
@test integrate(x*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(1//6*a^-2*log(1+-1*a^2*x^2)+1//12*a^-2*(1+-1*a^2*x^2)+-1//4*a^-2*(1+-1*a^2*x^2)^2*arctanh(a*x)^2+1//3*x*a^-1*arctanh(a*x)+1//6*x*a^-1*(1+-1*a^2*x^2)*arctanh(a*x))
@test integrate(arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(-1//3*x+-2//3*a^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+2//3*x*arctanh(a*x)^2+2//3*a^-1*arctanh(a*x)^2+-4//3*a^-1*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+1//3*x*arctanh(a*x)^2*(1+-1*a^2*x^2)+1//3*a^-1*(1+-1*a^2*x^2)*arctanh(a*x))
@test integrate(x^-1*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :((1/2)*arctanh(a*x)^2+(1/2)*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-1//2*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+-1//2*log(1+-1*a^2*x^2)+Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)*arctanh(a*x)+-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+2*arctanh(a*x)^2*arctanh(1+-2*(1+-1*a*x)^-1)+-1*a*x*arctanh(a*x)+-1//2*a^2*x^2*arctanh(a*x)^2)
@test integrate(x^-2*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(a*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-1*a*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1*x^-1*arctanh(a*x)^2+-1*x*a^2*arctanh(a*x)^2+2*a*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+2*a*arctanh(a*x)*log(2+-2*(1+a*x)^-1))
@test integrate(x^-3*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(a^2*log(x)+(1/2)*a^2*arctanh(a*x)^2+(1/2)*a^2*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+-1//2*a^2*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-1//2*a^2*log(1+-1*a^2*x^2)+-1//2*x^-2*arctanh(a*x)^2+a^2*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-1*a*x^-1*arctanh(a*x)+-1*a^2*Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)*arctanh(a*x)+-2*a^2*arctanh(a*x)^2*arctanh(1+-2*(1+-1*a*x)^-1))
@test integrate(x^-4*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(-2//3*a^3*arctanh(a*x)^2+-1//3*a^2*x^-1+-1//3*x^-3*arctanh(a*x)^2+1//3*a^3*arctanh(a*x)+2//3*a^3*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+a^2*x^-1*arctanh(a*x)^2+-4//3*a^3*arctanh(a*x)*log(2+-2*(1+a*x)^-1)+-1//3*a*x^-2*arctanh(a*x))
@test integrate(x^-5*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(-1//3*a^4*log(x)+-1//12*a^2*x^-2+1//6*a^4*log(1+-1*a^2*x^2)+(1/2)*a^3*x^-1*arctanh(a*x)+-1//4*x^-4*(1+-1*a^2*x^2)^2*arctanh(a*x)^2+-1//6*a*x^-3*arctanh(a*x))
@test integrate(x^-6*arctanh(a*x)^2*(1+-1*a^2*x^2), x) == :(-2//15*a^5*arctanh(a*x)^2+-1//5*x^-5*arctanh(a*x)^2+-1//30*a^2*x^-3+-1//30*a^5*arctanh(a*x)+1//30*a^4*x^-1+2//15*a^5*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-4//15*a^5*arctanh(a*x)*log(2+-2*(1+a*x)^-1)+-1//10*a*x^-4*arctanh(a*x)+1//3*a^2*x^-3*arctanh(a*x)^2+2//15*a^3*x^-2*arctanh(a*x))
@test integrate(arctanh(a*x)^3*(1+-1*a^2*x^2), x) == :(a^-1*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-1*x*arctanh(a*x)+-1//2*a^-1*log(1+-1*a^2*x^2)+2//3*x*arctanh(a*x)^3+2//3*a^-1*arctanh(a*x)^3+(1/2)*a^-1*arctanh(a*x)^2*(1+-1*a^2*x^2)+-2*a^-1*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+-2*a^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+1//3*x*arctanh(a*x)^3*(1+-1*a^2*x^2))
@test integrate(x*(1+-1*x^2)^-1*arctanh((1/2)*x*2^(1/2)), x) == :(-1//2*Polylogarithms.polylog(2,1+-2*2^(1/2)*(x+2^(1/2))^-1)+1//4*Polylogarithms.polylog(2,1+(2+-1*2^(1/2))^-1*(x+2^(1/2))^-1*(4+-4x))+1//4*Polylogarithms.polylog(2,1+-1*(2+2^(1/2))^-1*(x+2^(1/2))^-1*(4+4x))+arctanh((1/2)*x*2^(1/2))*log(2*2^(1/2)*(x+2^(1/2))^-1)+-1//2*arctanh((1/2)*x*2^(1/2))*log((2+2^(1/2))^-1*(x+2^(1/2))^-1*(4+4x))+-1//2*arctanh((1/2)*x*2^(1/2))*log(-1*(2+-1*2^(1/2))^-1*(x+2^(1/2))^-1*(4+-4x)))
@test integrate(x^4*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :(-11//378*a*x^6+1//5*x^5*arctanh(a*x)+1//72*a^3*x^8+2//315*a^-1*x^4+4//315*a^-5*log(1+-1*a^2*x^2)+4//315*a^-3*x^2+-2//7*a^2*x^7*arctanh(a*x)+1//9*a^4*x^9*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :(-1//24*a*x^5+-1//24*a^-4*arctanh(a*x)+1//4*x^4*arctanh(a*x)+1//24*x*a^-3+1//56*a^3*x^7+1//72*a^-1*x^3+-1//3*a^2*x^6*arctanh(a*x)+1//8*a^4*x^8*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :(-9//140*a*x^4+1//3*x^3*arctanh(a*x)+1//42*a^3*x^6+4//105*a^-1*x^2+4//105*a^-3*log(1+-1*a^2*x^2)+-2//5*a^2*x^5*arctanh(a*x)+1//7*a^4*x^7*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :(-1//9*a*x^3+1//6*x*a^-1+1//30*a^3*x^5+-1//6*a^-2*(1+-1*a^2*x^2)^3*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^2*arctanh(a*x), x) == :(1//15*a^-1*(2+-2*a^2*x^2)+1//20*a^-1*(1+-1*a^2*x^2)^2+4//15*a^-1*log(1+-1*a^2*x^2)+8//15*x*arctanh(a*x)+1//5*x*(1+-1*a^2*x^2)^2*arctanh(a*x)+4//15*x*(1+-1*a^2*x^2)*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :((1/2)*Polylogarithms.polylog(2,a*x)+-1//2*Polylogarithms.polylog(2,-1*a*x)+3//4*arctanh(a*x)+-3//4*a*x+1//12*a^3*x^3+-1*a^2*x^2*arctanh(a*x)+1//4*a^4*x^4*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :(a*log(x)+-1*x^-1*arctanh(a*x)+-4//3*a*log(1+-1*a^2*x^2)+1//6*a^3*x^2+-2*x*a^2*arctanh(a*x)+1//3*a^4*x^3*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :(a^2*Polylogarithms.polylog(2,-1*a*x)+(1/2)*x*a^3+-1*a^2*Polylogarithms.polylog(2,a*x)+-1//2*a*x^-1+-1//2*x^-2*arctanh(a*x)+(1/2)*a^4*x^2*arctanh(a*x))
@test integrate(x^-4*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :(-5//3*a^3*log(x)+-1//3*x^-3*arctanh(a*x)+-1//6*a*x^-2+4//3*a^3*log(1+-1*a^2*x^2)+x*a^4*arctanh(a*x)+2*a^2*x^-1*arctanh(a*x))
@test integrate(x^-5*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :((1/2)*a^4*Polylogarithms.polylog(2,a*x)+-3//4*a^4*arctanh(a*x)+-1//2*a^4*Polylogarithms.polylog(2,-1*a*x)+-1//4*x^-4*arctanh(a*x)+-1//12*a*x^-3+3//4*a^3*x^-1+a^2*x^-2*arctanh(a*x))
@test integrate(x^-6*(1+-1*a^2*x^2)^2*arctanh(a*x), x) == :(-4//15*a^5*log(1+-1*a^2*x^2)+-1//5*x^-5*arctanh(a*x)+-1//20*a*x^-4+7//30*a^3*x^-2+8//15*a^5*log(x)+-1*a^4*x^-1*arctanh(a*x)+2//3*a^2*x^-3*arctanh(a*x))
@test integrate(x^4*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-23//3780*x^5+-67//11340*a^-2*x^3+-29//3780*a^-5*arctanh(a*x)+-8//315*a^-5*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+1//5*x^5*arctanh(a*x)^2+1//252*a^2*x^7+8//315*a^-5*arctanh(a*x)^2+29//3780*x*a^-4+-16//315*a^-5*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+-11//189*a*x^6*arctanh(a*x)+-2//7*a^2*x^7*arctanh(a*x)^2+1//9*a^4*x^9*arctanh(a*x)^2+1//36*a^3*x^8*arctanh(a*x)+4//315*a^-1*x^4*arctanh(a*x)+8//315*a^-3*x^2*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-1//84*x^4+-5//504*a^-2*x^2+-1//24*a^-4*arctanh(a*x)^2+1//4*x^4*arctanh(a*x)^2+1//168*a^2*x^6+2//63*a^-4*log(1+-1*a^2*x^2)+-1//3*a^2*x^6*arctanh(a*x)^2+-1//12*a*x^5*arctanh(a*x)+1//8*a^4*x^8*arctanh(a*x)^2+1//12*x*a^-3*arctanh(a*x)+1//28*a^3*x^7*arctanh(a*x)+1//36*a^-1*x^3*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-17//630*x^3+-8//105*a^-3*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-1//210*x*a^-2+1//3*x^3*arctanh(a*x)^2+1//105*a^2*x^5+1//210*a^-3*arctanh(a*x)+8//105*a^-3*arctanh(a*x)^2+-16//105*a^-3*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+-9//70*a*x^4*arctanh(a*x)+-2//5*a^2*x^5*arctanh(a*x)^2+1//7*a^4*x^7*arctanh(a*x)^2+1//21*a^3*x^6*arctanh(a*x)+8//105*a^-1*x^2*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(1//45*a^-2*(2+-2*a^2*x^2)+1//60*a^-2*(1+-1*a^2*x^2)^2+4//45*a^-2*log(1+-1*a^2*x^2)+-1//6*a^-2*(1+-1*a^2*x^2)^3*arctanh(a*x)^2+8//45*x*a^-1*arctanh(a*x)+1//15*x*a^-1*(1+-1*a^2*x^2)^2*arctanh(a*x)+4//45*x*a^-1*(1+-1*a^2*x^2)*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-11//30*x+-8//15*a^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+1//30*a^2*x^3+8//15*x*arctanh(a*x)^2+8//15*a^-1*arctanh(a*x)^2+-16//15*a^-1*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+1//5*x*(1+-1*a^2*x^2)^2*arctanh(a*x)^2+1//10*a^-1*(1+-1*a^2*x^2)^2*arctanh(a*x)+1//15*a^-1*(4+-4*a^2*x^2)*arctanh(a*x)+4//15*x*arctanh(a*x)^2*(1+-1*a^2*x^2))
@test integrate(x^-1*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :((1/2)*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-2//3*log(1+-1*a^2*x^2)+-1//2*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+3//4*arctanh(a*x)^2+Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)*arctanh(a*x)+-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+2*arctanh(a*x)^2*arctanh(1+-2*(1+-1*a*x)^-1)+1//12*a^2*x^2+-1*a^2*x^2*arctanh(a*x)^2+-3//2*a*x*arctanh(a*x)+1//4*a^4*x^4*arctanh(a*x)^2+1//6*a^3*x^3*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-1*a*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1*x^-1*arctanh(a*x)^2+-2//3*a*arctanh(a*x)^2+-1//3*a*arctanh(a*x)+1//3*x*a^2+5//3*a*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-2*x*a^2*arctanh(a*x)^2+2*a*arctanh(a*x)*log(2+-2*(1+a*x)^-1)+1//3*a^3*x^2*arctanh(a*x)+1//3*a^4*x^3*arctanh(a*x)^2+10//3*a*arctanh(a*x)*log(2*(1+-1*a*x)^-1))
@test integrate(x^-3*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(a^2*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+a^2*log(x)+-1*a^2*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-1//2*x^-2*arctanh(a*x)^2+x*a^3*arctanh(a*x)+(1/2)*a^4*x^2*arctanh(a*x)^2+-1*a*x^-1*arctanh(a*x)+-4*a^2*arctanh(a*x)^2*arctanh(1+-2*(1+-1*a*x)^-1)+-2*a^2*Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)*arctanh(a*x)+2*a^2*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x))
@test integrate(x^-4*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-1*a^3*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-2//3*a^3*arctanh(a*x)^2+-1//3*a^2*x^-1+-1//3*x^-3*arctanh(a*x)^2+1//3*a^3*arctanh(a*x)+5//3*a^3*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+x*a^4*arctanh(a*x)^2+-2*a^3*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+2*a^2*x^-1*arctanh(a*x)^2+-10//3*a^3*arctanh(a*x)*log(2+-2*(1+a*x)^-1)+-1//3*a*x^-2*arctanh(a*x))
@test integrate(x^-5*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :((1/2)*a^4*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-4//3*a^4*log(x)+-3//4*a^4*arctanh(a*x)^2+-1//2*a^4*Polylogarithms.polylog(3,-1+2*(1+-1*a*x)^-1)+-1//4*x^-4*arctanh(a*x)^2+-1//12*a^2*x^-2+2//3*a^4*log(1+-1*a^2*x^2)+a^2*x^-2*arctanh(a*x)^2+a^4*Polylogarithms.polylog(2,-1+2*(1+-1*a*x)^-1)*arctanh(a*x)+-1*a^4*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+2*a^4*arctanh(a*x)^2*arctanh(1+-2*(1+-1*a*x)^-1)+-1//6*a*x^-3*arctanh(a*x)+3//2*a^3*x^-1*arctanh(a*x))
@test integrate(x^-6*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-11//30*a^5*arctanh(a*x)+-8//15*a^5*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1//5*x^-5*arctanh(a*x)^2+-1//30*a^2*x^-3+8//15*a^5*arctanh(a*x)^2+11//30*a^4*x^-1+-1*a^4*x^-1*arctanh(a*x)^2+-1//10*a*x^-4*arctanh(a*x)+2//3*a^2*x^-3*arctanh(a*x)^2+7//15*a^3*x^-2*arctanh(a*x)+16//15*a^5*arctanh(a*x)*log(2+-2*(1+a*x)^-1))
@test integrate(x^-7*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-4//45*a^6*log(1+-1*a^2*x^2)+-1//60*a^2*x^-4+7//90*a^4*x^-2+8//45*a^6*log(x)+-1//3*a^5*x^-1*arctanh(a*x)+-1//6*x^-6*(1+-1*a^2*x^2)^3*arctanh(a*x)^2+-1//15*a*x^-5*arctanh(a*x)+2//9*a^3*x^-3*arctanh(a*x))
@test integrate(x^-8*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-8//105*a^7*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1//7*x^-7*arctanh(a*x)^2+-1//105*a^2*x^-5+-1//210*a^7*arctanh(a*x)+1//210*a^6*x^-1+8//105*a^7*arctanh(a*x)^2+17//630*a^4*x^-3+-8//105*a^5*x^-2*arctanh(a*x)+-1//3*a^4*x^-3*arctanh(a*x)^2+-1//21*a*x^-6*arctanh(a*x)+2//5*a^2*x^-5*arctanh(a*x)^2+9//70*a^3*x^-4*arctanh(a*x)+16//105*a^7*arctanh(a*x)*log(2+-2*(1+a*x)^-1))
@test integrate(x^-9*(1+-1*a^2*x^2)^2*arctanh(a*x)^2, x) == :(-2//63*a^8*log(1+-1*a^2*x^2)+-1//8*x^-8*arctanh(a*x)^2+-1//168*a^2*x^-6+1//24*a^8*arctanh(a*x)^2+1//84*a^4*x^-4+4//63*a^8*log(x)+5//504*a^6*x^-2+-1//4*a^4*x^-4*arctanh(a*x)^2+-1//12*a^7*x^-1*arctanh(a*x)+-1//28*a*x^-7*arctanh(a*x)+-1//36*a^5*x^-3*arctanh(a*x)+1//3*a^2*x^-6*arctanh(a*x)^2+1//12*a^3*x^-5*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^2*arctanh(a*x)^3, x) == :(-1*x*arctanh(a*x)+-1//2*a^-1*log(1+-1*a^2*x^2)+-1//20*a^-1*(1+-1*a^2*x^2)+4//5*a^-1*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+8//15*x*arctanh(a*x)^3+8//15*a^-1*arctanh(a*x)^3+-8//5*a^-1*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+-8//5*a^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-1//10*x*(1+-1*a^2*x^2)*arctanh(a*x)+1//5*x*(1+-1*a^2*x^2)^2*arctanh(a*x)^3+1//5*a^-1*arctanh(a*x)^2*(2+-2*a^2*x^2)+3//20*a^-1*(1+-1*a^2*x^2)^2*arctanh(a*x)^2+4//15*x*arctanh(a*x)^3*(1+-1*a^2*x^2))
@test integrate((1+-1*a^2*x^2)^3*arctanh(a*x), x) == :(1//35*a^-1*(4+-4*a^2*x^2)+1//42*a^-1*(1+-1*a^2*x^2)^3+3//70*a^-1*(1+-1*a^2*x^2)^2+8//35*a^-1*log(1+-1*a^2*x^2)+16//35*x*arctanh(a*x)+1//7*x*(1+-1*a^2*x^2)^3*arctanh(a*x)+6//35*x*(1+-1*a^2*x^2)^2*arctanh(a*x)+8//35*x*(1+-1*a^2*x^2)*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^3*arctanh(a*x)^2, x) == :(-38//105*x+-16//35*a^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-1//105*a^4*x^5+16//35*x*arctanh(a*x)^2+16//35*a^-1*arctanh(a*x)^2+19//315*a^2*x^3+-32//35*a^-1*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+1//7*x*(1+-1*a^2*x^2)^3*arctanh(a*x)^2+1//21*a^-1*(1+-1*a^2*x^2)^3*arctanh(a*x)+1//35*a^-1*(8+-8*a^2*x^2)*arctanh(a*x)+3//35*a^-1*(1+-1*a^2*x^2)^2*arctanh(a*x)+6//35*x*(1+-1*a^2*x^2)^2*arctanh(a*x)^2+8//35*x*arctanh(a*x)^2*(1+-1*a^2*x^2))
@test integrate((1+-1*a^2*x^2)^3*arctanh(a*x)^3, x) == :(-14//15*x*arctanh(a*x)+-7//15*a^-1*log(1+-1*a^2*x^2)+-1//140*a^-1*(1+-1*a^2*x^2)^2+-1//210*a^-1*(13+-13*a^2*x^2)+16//35*x*arctanh(a*x)^3+16//35*a^-1*arctanh(a*x)^3+24//35*a^-1*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-48//35*a^-1*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+-48//35*a^-1*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-13//105*x*(1+-1*a^2*x^2)*arctanh(a*x)+-1//35*x*(1+-1*a^2*x^2)^2*arctanh(a*x)+1//7*x*(1+-1*a^2*x^2)^3*arctanh(a*x)^3+1//14*a^-1*(1+-1*a^2*x^2)^3*arctanh(a*x)^2+1//35*a^-1*arctanh(a*x)^2*(12+-12*a^2*x^2)+6//35*x*(1+-1*a^2*x^2)^2*arctanh(a*x)^3+8//35*x*arctanh(a*x)^3*(1+-1*a^2*x^2)+9//70*a^-1*(1+-1*a^2*x^2)^2*arctanh(a*x)^2)
@test integrate(x^3*(1+-1*a^2*x^2)^-1*arctanh(a*x), x) == :((1/2)*a^-4*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+(1/2)*a^-4*arctanh(a*x)+-1//2*x*a^-3+-1//2*a^-4*arctanh(a*x)^2+a^-4*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+-1//2*a^-2*x^2*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-1*arctanh(a*x), x) == :((1/2)*a^-3*arctanh(a*x)^2+-1//2*a^-3*log(1+-1*a^2*x^2)+-1*x*a^-2*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-1*arctanh(a*x), x) == :((1/2)*a^-2*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-1//2*a^-2*arctanh(a*x)^2+a^-2*arctanh(a*x)*log(2*(1+-1*a*x)^-1))
@test integrate((1+-1*a^2*x^2)^-1*arctanh(a*x), x) == :((1/2)*a^-1*arctanh(a*x)^2)
@test integrate(x^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x), x) == :((1/2)*arctanh(a*x)^2+-1//2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+arctanh(a*x)*log(2+-2*(1+a*x)^-1))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x), x) == :(a*log(x)+(1/2)*a*arctanh(a*x)^2+-1*x^-1*arctanh(a*x)+-1//2*a*log(1+-1*a^2*x^2))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x), x) == :((1/2)*a^2*arctanh(a*x)^2+(1/2)*a^2*arctanh(a*x)+-1//2*a*x^-1+-1//2*a^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1//2*x^-2*arctanh(a*x)+a^2*arctanh(a*x)*log(2+-2*(1+a*x)^-1))
@test integrate(x^3*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2, x) == :((1/2)*a^-4*arctanh(a*x)^2+-1//2*a^-4*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-1//2*a^-4*log(1+-1*a^2*x^2)+-1//3*a^-4*arctanh(a*x)^3+a^-4*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+a^-4*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-1*x*a^-3*arctanh(a*x)+-1//2*a^-2*x^2*arctanh(a*x)^2)
@test integrate(x^2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2, x) == :(a^-3*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-1*a^-3*arctanh(a*x)^2+1//3*a^-3*arctanh(a*x)^3+-1*x*a^-2*arctanh(a*x)^2+2*a^-3*arctanh(a*x)*log(2*(1+-1*a*x)^-1))
@test integrate(x*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2, x) == :(-1//2*a^-2*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-1//3*a^-2*arctanh(a*x)^3+a^-2*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+a^-2*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-1*arctanh(a*x)^2, x) == :(1//3*a^-1*arctanh(a*x)^3)
@test integrate(x^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2, x) == :(-1//2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+1//3*arctanh(a*x)^3+arctanh(a*x)^2*log(2+-2*(1+a*x)^-1)+-1*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2, x) == :(a*arctanh(a*x)^2+-1*a*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1*x^-1*arctanh(a*x)^2+1//3*a*arctanh(a*x)^3+2*a*arctanh(a*x)*log(2+-2*(1+a*x)^-1))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2, x) == :(a^2*log(x)+(1/2)*a^2*arctanh(a*x)^2+-1//2*a^2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+-1//2*a^2*log(1+-1*a^2*x^2)+-1//2*x^-2*arctanh(a*x)^2+1//3*a^2*arctanh(a*x)^3+a^2*arctanh(a*x)^2*log(2+-2*(1+a*x)^-1)+-1*a*x^-1*arctanh(a*x)+-1*a^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3, x) == :((1/2)*a^-4*arctanh(a*x)^3+-3//2*a^-4*arctanh(a*x)^2+-1//4*a^-4*arctanh(a*x)^4+3//2*a^-4*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+3//4*a^-4*Polylogarithms.polylog(4,1+-2*(1+-1*a*x)^-1)+a^-4*arctanh(a*x)^3*log(2*(1+-1*a*x)^-1)+3*a^-4*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+-3//2*x*a^-3*arctanh(a*x)^2+-3//2*a^-4*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-1//2*a^-2*x^2*arctanh(a*x)^3+3//2*a^-4*arctanh(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1))
@test integrate(x^2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3, x) == :(-1*a^-3*arctanh(a*x)^3+-3//2*a^-3*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+1//4*a^-3*arctanh(a*x)^4+-1*x*a^-2*arctanh(a*x)^3+3*a^-3*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+3*a^-3*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3, x) == :(-1//4*a^-2*arctanh(a*x)^4+3//4*a^-2*Polylogarithms.polylog(4,1+-2*(1+-1*a*x)^-1)+a^-2*arctanh(a*x)^3*log(2*(1+-1*a*x)^-1)+-3//2*a^-2*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+3//2*a^-2*arctanh(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1))
@test integrate((1+-1*a^2*x^2)^-1*arctanh(a*x)^3, x) == :(1//4*a^-1*arctanh(a*x)^4)
@test integrate(x^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3, x) == :(-3//4*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+1//4*arctanh(a*x)^4+arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+-3//2*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3, x) == :(a*arctanh(a*x)^3+-1*x^-1*arctanh(a*x)^3+-3//2*a*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+1//4*a*arctanh(a*x)^4+-3*a*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x)+3*a*arctanh(a*x)^2*log(2+-2*(1+a*x)^-1))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3, x) == :((1/2)*a^2*arctanh(a*x)^3+-3//2*a^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//4*a^2*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+-1//2*x^-2*arctanh(a*x)^3+1//4*a^2*arctanh(a*x)^4+3//2*a^2*arctanh(a*x)^2+a^2*arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+3*a^2*arctanh(a*x)*log(2+-2*(1+a*x)^-1)+-3//2*a*x^-1*arctanh(a*x)^2+-3//2*a^2*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//2*a^2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-1*arctanh(a*x)^(1/2), x) == :(2//3*a^-1*arctanh(a*x)^3//2)
@test integrate((1+-1*a^2*x^2)^-1*arctanh(a*x)^-1, x) == :(a^-1*log(arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-1*arctanh(a*x)^-2, x) == :(-1*a^-1*arctanh(a*x)^-1)
@test integrate((1+-1*a^2*x^2)^-1*arctanh(a*x)^-3, x) == :(-1//2*a^-1*arctanh(a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-1*arctanh(a*x)^p, x) == :(a^-1*(1+p)^-1*arctanh(a*x)^(1+p))
@test integrate(x^3*(1+-1*a^2*x^2)^-2*arctanh(a*x), x) == :((1/2)*a^-4*arctanh(a*x)^2+-1//2*a^-4*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-1//4*a^-4*arctanh(a*x)+(1/2)*a^-4*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-1*a^-4*arctanh(a*x)*log(2*(1+-1*a*x)^-1)+-1//4*x*a^-3*(1+-1*a^2*x^2)^-1)
@test integrate(x^2*(1+-1*a^2*x^2)^-2*arctanh(a*x), x) == :(-1//4*a^-3*(1+-1*a^2*x^2)^-1+-1//4*a^-3*arctanh(a*x)^2+(1/2)*x*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-2*arctanh(a*x), x) == :(-1//4*a^-2*arctanh(a*x)+(1/2)*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-1//4*x*a^-1*(1+-1*a^2*x^2)^-1)
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x), x) == :(-1//4*a^-1*(1+-1*a^2*x^2)^-1+1//4*a^-1*arctanh(a*x)^2+x*(2+-2*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x), x) == :((1/2)*arctanh(a*x)^2+-1//2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1//4*arctanh(a*x)+(2+-2*a^2*x^2)^-1*arctanh(a*x)+arctanh(a*x)*log(2+-2*(1+a*x)^-1)+-1*a*x*(4+-4*a^2*x^2)^-1)
@test integrate(x^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x), x) == :(a*log(x)+-1*a*(4+-4*a^2*x^2)^-1+-1*x^-1*arctanh(a*x)+-1//2*a*log(1+-1*a^2*x^2)+3//4*a*arctanh(a*x)^2+x*a^2*(2+-2*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-2*arctanh(a*x), x) == :(a^2*arctanh(a*x)^2+-1*a^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1//2*a*x^-1+-1//2*x^-2*arctanh(a*x)+1//4*a^2*arctanh(a*x)+a^2*(2+-2*a^2*x^2)^-1*arctanh(a*x)+-1*x*a^3*(4+-4*a^2*x^2)^-1+2*a^2*arctanh(a*x)*log(2+-2*(1+a*x)^-1))
@test integrate(x^3*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2, x) == :((1/2)*a^-4*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)+-1//4*a^-4*arctanh(a*x)^2+1//3*a^-4*arctanh(a*x)^3+1//4*a^-4*(1+-1*a^2*x^2)^-1+(1/2)*a^-4*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2+-1*a^-4*arctanh(a*x)^2*log(2*(1+-1*a*x)^-1)+-1*a^-4*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+-1//2*x*a^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2, x) == :(-1//6*a^-3*arctanh(a*x)^3+1//4*a^-3*arctanh(a*x)+-1//2*a^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x)+1//4*x*a^-2*(1+-1*a^2*x^2)^-1+(1/2)*x*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2)
@test integrate(x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2, x) == :(-1//4*a^-2*arctanh(a*x)^2+1//4*a^-2*(1+-1*a^2*x^2)^-1+(1/2)*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2+-1//2*x*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^2, x) == :(x*(4+-4*a^2*x^2)^-1+1//4*a^-1*arctanh(a*x)+1//6*a^-1*arctanh(a*x)^3+x*(2+-2*a^2*x^2)^-1*arctanh(a*x)^2+-1//2*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2, x) == :((4+-4*a^2*x^2)^-1+-1//2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+-1//4*arctanh(a*x)^2+1//3*arctanh(a*x)^3+(2+-2*a^2*x^2)^-1*arctanh(a*x)^2+arctanh(a*x)^2*log(2+-2*(1+a*x)^-1)+-1*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x)+-1*a*x*(2+-2*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2, x) == :(a*arctanh(a*x)^2+(1/2)*a*arctanh(a*x)^3+-1*a*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1*x^-1*arctanh(a*x)^2+1//4*a*arctanh(a*x)+x*a^2*(4+-4*a^2*x^2)^-1+-1*a*(2+-2*a^2*x^2)^-1*arctanh(a*x)+2*a*arctanh(a*x)*log(2+-2*(1+a*x)^-1)+x*a^2*(2+-2*a^2*x^2)^-1*arctanh(a*x)^2)
@test integrate(x^-3*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2, x) == :(a^2*(4+-4*a^2*x^2)^-1+a^2*log(x)+-1*a^2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+-1//2*a^2*log(1+-1*a^2*x^2)+-1//2*x^-2*arctanh(a*x)^2+1//4*a^2*arctanh(a*x)^2+2//3*a^2*arctanh(a*x)^3+a^2*(2+-2*a^2*x^2)^-1*arctanh(a*x)^2+-1*a*x^-1*arctanh(a*x)+-2*a^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x)+2*a^2*arctanh(a*x)^2*log(2+-2*(1+a*x)^-1)+-1*x*a^3*(2+-2*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3, x) == :(-3//4*a^-4*Polylogarithms.polylog(4,1+-2*(1+-1*a*x)^-1)+-3//8*a^-4*arctanh(a*x)+-1//4*a^-4*arctanh(a*x)^3+1//4*a^-4*arctanh(a*x)^4+(1/2)*a^-4*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3+-1*a^-4*arctanh(a*x)^3*log(2*(1+-1*a*x)^-1)+-3//2*a^-4*arctanh(a*x)^2*Polylogarithms.polylog(2,1+-2*(1+-1*a*x)^-1)+-3//8*x*a^-3*(1+-1*a^2*x^2)^-1+3//2*a^-4*Polylogarithms.polylog(3,1+-2*(1+-1*a*x)^-1)*arctanh(a*x)+3//4*a^-4*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-3//4*x*a^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2)
@test integrate(x^2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3, x) == :(-3//8*a^-3*(1+-1*a^2*x^2)^-1+-1//8*a^-3*arctanh(a*x)^4+3//8*a^-3*arctanh(a*x)^2+-3//4*a^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2+(1/2)*x*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3+3//4*x*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3, x) == :(-3//8*a^-2*arctanh(a*x)+-1//4*a^-2*arctanh(a*x)^3+(1/2)*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3+-3//8*x*a^-1*(1+-1*a^2*x^2)^-1+3//4*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-3//4*x*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2)
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^3, x) == :(-3//8*a^-1*(1+-1*a^2*x^2)^-1+1//8*a^-1*arctanh(a*x)^4+3//8*a^-1*arctanh(a*x)^2+x*(2+-2*a^2*x^2)^-1*arctanh(a*x)^3+3*x*(4+-4*a^2*x^2)^-1*arctanh(a*x)+-3//4*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2)
@test integrate(x^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3, x) == :(-3//4*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+-3//8*arctanh(a*x)+-1//4*arctanh(a*x)^3+1//4*arctanh(a*x)^4+(2+-2*a^2*x^2)^-1*arctanh(a*x)^3+arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+3*(4+-4*a^2*x^2)^-1*arctanh(a*x)+-3//2*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x)+-3*a*x*(8+-8*a^2*x^2)^-1+-3*a*x*(4+-4*a^2*x^2)^-1*arctanh(a*x)^2)
@test integrate(x^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3, x) == :(a*arctanh(a*x)^3+-1*x^-1*arctanh(a*x)^3+-3*a*(8+-8*a^2*x^2)^-1+-3//2*a*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+3//8*a*arctanh(a*x)^2+3//8*a*arctanh(a*x)^4+-3*a*(4+-4*a^2*x^2)^-1*arctanh(a*x)^2+-3*a*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x)+3*a*arctanh(a*x)^2*log(2+-2*(1+a*x)^-1)+x*a^2*(2+-2*a^2*x^2)^-1*arctanh(a*x)^3+3*x*a^2*(4+-4*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3, x) == :((1/2)*a^2*arctanh(a*x)^4+-3//2*a^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//2*a^2*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+-3//8*a^2*arctanh(a*x)+-1//2*x^-2*arctanh(a*x)^3+1//4*a^2*arctanh(a*x)^3+3//2*a^2*arctanh(a*x)^2+a^2*(2+-2*a^2*x^2)^-1*arctanh(a*x)^3+-3*x*a^3*(8+-8*a^2*x^2)^-1+-3*a^2*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3*a^2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x)+2*a^2*arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+3*a^2*(4+-4*a^2*x^2)^-1*arctanh(a*x)+3*a^2*arctanh(a*x)*log(2+-2*(1+a*x)^-1)+-3//2*a*x^-1*arctanh(a*x)^2+-3*x*a^3*(4+-4*a^2*x^2)^-1*arctanh(a*x)^2)
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^(1/2), x) == :(1//3*a^-1*arctanh(a*x)^3//2+x*(2+-2*a^2*x^2)^-1*arctanh(a*x)^(1/2)+-1//32*2^(1/2)*pi^(1/2)*a^-1*erfi(2^(1/2)*arctanh(a*x)^(1/2))+1//32*2^(1/2)*pi^(1/2)*a^-1*erf(2^(1/2)*arctanh(a*x)^(1/2)))
@test integrate(x^2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1, x) == :((1/2)*a^-3*coshintegral(2*arctanh(a*x))+-1//2*a^-3*log(arctanh(a*x)))
@test integrate(x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1, x) == :((1/2)*a^-2*sinhintegral(2*arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^-1, x) == :((1/2)*a^-1*coshintegral(2*arctanh(a*x))+(1/2)*a^-1*log(arctanh(a*x)))
@test integrate(x^2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-2, x) == :(a^-3*sinhintegral(2*arctanh(a*x))+-1*a^-1*x^2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1)
@test integrate(x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-2, x) == :(a^-2*coshintegral(2*arctanh(a*x))+-1*x*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1)
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^-2, x) == :(a^-1*sinhintegral(2*arctanh(a*x))+-1*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1)
@test integrate(x^2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-3, x) == :(a^-3*coshintegral(2*arctanh(a*x))+-1*x*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1+-1//2*a^-1*x^2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-2)
@test integrate(x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-3, x) == :(a^-2*sinhintegral(2*arctanh(a*x))+-1//2*x*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-2+-1//2*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1*(1+a^2*x^2))
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^-3, x) == :(a^-1*coshintegral(2*arctanh(a*x))+-1*x*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1+-1//2*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^-4, x) == :(2//3*a^-1*sinhintegral(2*arctanh(a*x))+-1*x*(3+-3*a^2*x^2)^-1*arctanh(a*x)^-2+-1//3*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-3+-1//3*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1*(1+a^2*x^2))
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^-5, x) == :(1//3*a^-1*coshintegral(2*arctanh(a*x))+-1*x*(3+-3*a^2*x^2)^-1*arctanh(a*x)^-1+-1*x*(6+-6*a^2*x^2)^-1*arctanh(a*x)^-3+-1//4*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-4+-1//12*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-2*(1+a^2*x^2))
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^-6, x) == :(2//15*a^-1*sinhintegral(2*arctanh(a*x))+-1*x*(10+-10*a^2*x^2)^-1*arctanh(a*x)^-4+-1*x*(15+-15*a^2*x^2)^-1*arctanh(a*x)^-2+-1//5*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-5+-1//15*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1*(1+a^2*x^2)+-1//30*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-3*(1+a^2*x^2))
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^-7, x) == :(2//45*a^-1*coshintegral(2*arctanh(a*x))+-1*x*(15+-15*a^2*x^2)^-1*arctanh(a*x)^-5+-1*x*(45+-45*a^2*x^2)^-1*arctanh(a*x)^-3+-2*x*(45+-45*a^2*x^2)^-1*arctanh(a*x)^-1+-1//6*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-6+-1//60*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-4*(1+a^2*x^2)+-1//90*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-2*(1+a^2*x^2))
@test integrate((1+-1*a^2*x^2)^-2*arctanh(a*x)^-8, x) == :(4//315*a^-1*sinhintegral(2*arctanh(a*x))+-1*x*(21+-21*a^2*x^2)^-1*arctanh(a*x)^-6+-1*x*(105+-105*a^2*x^2)^-1*arctanh(a*x)^-4+-2*x*(315+-315*a^2*x^2)^-1*arctanh(a*x)^-2+-1//7*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-7+-1//105*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-5*(1+a^2*x^2)+-1//315*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1*(2+2*a^2*x^2)+-1//315*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-3*(1+a^2*x^2))
@test integrate(x^3*(1+-1*a^2*x^2)^-3*arctanh(a*x), x) == :(-3//32*a^-4*arctanh(a*x)+-1//16*a^-1*x^3*(1+-1*a^2*x^2)^-2+1//4*x^4*(1+-1*a^2*x^2)^-2*arctanh(a*x)+3//32*x*a^-3*(1+-1*a^2*x^2)^-1)
@test integrate(x^2*(1+-1*a^2*x^2)^-3*arctanh(a*x), x) == :(-1//16*a^-3*(1+-1*a^2*x^2)^-2+-1//16*a^-3*arctanh(a*x)^2+1//16*a^-3*(1+-1*a^2*x^2)^-1+-1//8*x*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)+1//4*x*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-3*arctanh(a*x), x) == :(-3//32*a^-2*arctanh(a*x)+-3//32*x*a^-1*(1+-1*a^2*x^2)^-1+-1//16*x*a^-1*(1+-1*a^2*x^2)^-2+1//4*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x), x) == :(-3//16*a^-1*(1+-1*a^2*x^2)^-1+-1//16*a^-1*(1+-1*a^2*x^2)^-2+3//16*a^-1*arctanh(a*x)^2+3*x*(8+-8*a^2*x^2)^-1*arctanh(a*x)+1//4*x*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-3*arctanh(a*x), x) == :((1/2)*arctanh(a*x)^2+-11//32*arctanh(a*x)+-1//2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+(2+-2*a^2*x^2)^-1*arctanh(a*x)+arctanh(a*x)*log(2+-2*(1+a*x)^-1)+1//4*(1+-1*a^2*x^2)^-2*arctanh(a*x)+-11*a*x*(32+-32*a^2*x^2)^-1+-1//16*a*x*(1+-1*a^2*x^2)^-2)
@test integrate(x^-2*(1+-1*a^2*x^2)^-3*arctanh(a*x), x) == :(a*log(x)+-1*x^-1*arctanh(a*x)+-7*a*(16+-16*a^2*x^2)^-1+-1//2*a*log(1+-1*a^2*x^2)+-1//16*a*(1+-1*a^2*x^2)^-2+15//16*a*arctanh(a*x)^2+7*x*a^2*(8+-8*a^2*x^2)^-1*arctanh(a*x)+1//4*x*a^2*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-3*arctanh(a*x)^2, x) == :(-3//32*a^-4*(1+-1*a^2*x^2)^-1+-3//32*a^-4*arctanh(a*x)^2+1//32*x^4*(1+-1*a^2*x^2)^-2+1//4*x^4*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2+-1//8*a^-1*x^3*(1+-1*a^2*x^2)^-2*arctanh(a*x)+3//16*x*a^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-3*arctanh(a*x)^2, x) == :(-1//24*a^-3*arctanh(a*x)^3+-1//64*a^-3*arctanh(a*x)+-1//8*a^-3*(1+-1*a^2*x^2)^-2*arctanh(a*x)+-1//64*x*a^-2*(1+-1*a^2*x^2)^-1+1//8*a^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x)+1//32*x*a^-2*(1+-1*a^2*x^2)^-2+-1//8*x*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2+1//4*x*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2)
@test integrate(x*(1+-1*a^2*x^2)^-3*arctanh(a*x)^2, x) == :(-3//32*a^-2*arctanh(a*x)^2+1//32*a^-2*(1+-1*a^2*x^2)^-2+3//32*a^-2*(1+-1*a^2*x^2)^-1+1//4*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2+-3//16*x*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-1//8*x*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x)^2, x) == :(15*x*(64+-64*a^2*x^2)^-1+1//8*a^-1*arctanh(a*x)^3+1//32*x*(1+-1*a^2*x^2)^-2+15//64*a^-1*arctanh(a*x)+3*x*(8+-8*a^2*x^2)^-1*arctanh(a*x)^2+-3//8*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-1//8*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)+1//4*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2)
@test integrate(x^-1*(1+-1*a^2*x^2)^-3*arctanh(a*x)^2, x) == :(11*(32+-32*a^2*x^2)^-1+-11//32*arctanh(a*x)^2+-1//2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+1//3*arctanh(a*x)^3+1//32*(1+-1*a^2*x^2)^-2+(2+-2*a^2*x^2)^-1*arctanh(a*x)^2+arctanh(a*x)^2*log(2+-2*(1+a*x)^-1)+-1*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x)+1//4*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2+-11*a*x*(16+-16*a^2*x^2)^-1*arctanh(a*x)+-1//8*a*x*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-3*arctanh(a*x)^2, x) == :(a*arctanh(a*x)^2+-1*a*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-1*x^-1*arctanh(a*x)^2+5//8*a*arctanh(a*x)^3+31//64*a*arctanh(a*x)+-7*a*(8+-8*a^2*x^2)^-1*arctanh(a*x)+2*a*arctanh(a*x)*log(2+-2*(1+a*x)^-1)+31*x*a^2*(64+-64*a^2*x^2)^-1+-1//8*a*(1+-1*a^2*x^2)^-2*arctanh(a*x)+1//32*x*a^2*(1+-1*a^2*x^2)^-2+7*x*a^2*(8+-8*a^2*x^2)^-1*arctanh(a*x)^2+1//4*x*a^2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2)
@test integrate(x^3*(1+-1*a^2*x^2)^-3*arctanh(a*x)^3, x) == :(-3//32*a^-4*arctanh(a*x)^3+27//256*a^-4*arctanh(a*x)+-9//32*a^-4*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-3//128*a^-1*x^3*(1+-1*a^2*x^2)^-2+1//4*x^4*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3+3//32*x^4*(1+-1*a^2*x^2)^-2*arctanh(a*x)+45//256*x*a^-3*(1+-1*a^2*x^2)^-1+-3//16*a^-1*x^3*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2+9//32*x*a^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2)
@test integrate(x^2*(1+-1*a^2*x^2)^-3*arctanh(a*x)^3, x) == :(-3//128*a^-3*(1+-1*a^2*x^2)^-2+-3//128*a^-3*arctanh(a*x)^2+-1//32*a^-3*arctanh(a*x)^4+3//128*a^-3*(1+-1*a^2*x^2)^-1+-3//16*a^-3*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2+3//16*a^-3*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2+-3//64*x*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-1//8*x*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^3+1//4*x*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3+3//32*x*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-3*arctanh(a*x)^3, x) == :(-45//256*a^-2*arctanh(a*x)+-3//32*a^-2*arctanh(a*x)^3+-45//256*x*a^-1*(1+-1*a^2*x^2)^-1+-3//128*x*a^-1*(1+-1*a^2*x^2)^-2+1//4*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3+3//32*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x)+9//32*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-9//32*x*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2+-3//16*x*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2)
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x)^3, x) == :(-45//128*a^-1*(1+-1*a^2*x^2)^-1+-3//128*a^-1*(1+-1*a^2*x^2)^-2+3//32*a^-1*arctanh(a*x)^4+45//128*a^-1*arctanh(a*x)^2+3*x*(8+-8*a^2*x^2)^-1*arctanh(a*x)^3+45*x*(64+-64*a^2*x^2)^-1*arctanh(a*x)+-9//16*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2+-3//16*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2+1//4*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3+3//32*x*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-3*arctanh(a*x)^3, x) == :(-141//256*arctanh(a*x)+-11//32*arctanh(a*x)^3+-3//4*Polylogarithms.polylog(4,-1+2*(1+a*x)^-1)+1//4*arctanh(a*x)^4+(2+-2*a^2*x^2)^-1*arctanh(a*x)^3+arctanh(a*x)^3*log(2+-2*(1+a*x)^-1)+33*(32+-32*a^2*x^2)^-1*arctanh(a*x)+-3//2*arctanh(a*x)^2*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)+-3//2*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)*arctanh(a*x)+1//4*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3+3//32*(1+-1*a^2*x^2)^-2*arctanh(a*x)+-141*a*x*(256+-256*a^2*x^2)^-1+-3//128*a*x*(1+-1*a^2*x^2)^-2+-33*a*x*(32+-32*a^2*x^2)^-1*arctanh(a*x)^2+-3//16*a*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2)
@test integrate(x^-2*(1+-1*a^2*x^2)^-3*arctanh(a*x)^3, x) == :(a*arctanh(a*x)^3+-1*x^-1*arctanh(a*x)^3+-93*a*(128+-128*a^2*x^2)^-1+-3//2*a*Polylogarithms.polylog(3,-1+2*(1+a*x)^-1)+-3//128*a*(1+-1*a^2*x^2)^-2+15//32*a*arctanh(a*x)^4+93//128*a*arctanh(a*x)^2+-21*a*(16+-16*a^2*x^2)^-1*arctanh(a*x)^2+-3*a*Polylogarithms.polylog(2,-1+2*(1+a*x)^-1)*arctanh(a*x)+3*a*arctanh(a*x)^2*log(2+-2*(1+a*x)^-1)+-3//16*a*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2+7*x*a^2*(8+-8*a^2*x^2)^-1*arctanh(a*x)^3+93*x*a^2*(64+-64*a^2*x^2)^-1*arctanh(a*x)+1//4*x*a^2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3+3//32*x*a^2*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x)^(1/2), x) == :(1//4*a^-1*arctanh(a*x)^3//2+-1//256*pi^(1/2)*a^-1*erfi(2*arctanh(a*x)^(1/2))+1//4*a^-1*arctanh(a*x)^(1/2)*sinh(2*arctanh(a*x))+1//32*a^-1*arctanh(a*x)^(1/2)*sinh(4*arctanh(a*x))+1//256*pi^(1/2)*a^-1*erf(2*arctanh(a*x)^(1/2))+-1//32*2^(1/2)*pi^(1/2)*a^-1*erfi(2^(1/2)*arctanh(a*x)^(1/2))+1//32*2^(1/2)*pi^(1/2)*a^-1*erf(2^(1/2)*arctanh(a*x)^(1/2)))
@test integrate(x^4*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-1, x) == :(-1//2*a^-5*coshintegral(2*arctanh(a*x))+1//8*a^-5*coshintegral(4*arctanh(a*x))+3//8*a^-5*log(arctanh(a*x)))
@test integrate(x^3*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-1, x) == :(-1//4*a^-4*sinhintegral(2*arctanh(a*x))+1//8*a^-4*sinhintegral(4*arctanh(a*x)))
@test integrate(x^2*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-1, x) == :(-1//8*a^-3*log(arctanh(a*x))+1//8*a^-3*coshintegral(4*arctanh(a*x)))
@test integrate(x*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-1, x) == :(1//4*a^-2*sinhintegral(2*arctanh(a*x))+1//8*a^-2*sinhintegral(4*arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x)^-1, x) == :((1/2)*a^-1*coshintegral(2*arctanh(a*x))+1//8*a^-1*coshintegral(4*arctanh(a*x))+3//8*a^-1*log(arctanh(a*x)))
@test integrate(x^4*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-2, x) == :((1/2)*a^-5*sinhintegral(4*arctanh(a*x))+-1*a^-5*sinhintegral(2*arctanh(a*x))+-1*a^-1*x^4*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1)
@test integrate(x*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-2, x) == :((1/2)*a^-2*coshintegral(2*arctanh(a*x))+(1/2)*a^-2*coshintegral(4*arctanh(a*x))+-1*x*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1)
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x)^-2, x) == :(a^-1*sinhintegral(2*arctanh(a*x))+(1/2)*a^-1*sinhintegral(4*arctanh(a*x))+-1*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1)
@test integrate(x^4*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-3, x) == :(a^-5*coshintegral(4*arctanh(a*x))+-1*a^-5*coshintegral(2*arctanh(a*x))+-2*x*a^-4*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1+2*x*a^-4*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1+-1//2*a^-1*x^4*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-2)
@test integrate(x*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-3, x) == :(a^-2*sinhintegral(4*arctanh(a*x))+(1/2)*a^-2*sinhintegral(2*arctanh(a*x))+-2*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1+3//2*a^-2*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1+-1//2*x*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x)^-3, x) == :(a^-1*coshintegral(2*arctanh(a*x))+a^-1*coshintegral(4*arctanh(a*x))+-2*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1+-1//2*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x)^-4, x) == :(2//3*a^-1*sinhintegral(2*arctanh(a*x))+4//3*a^-1*sinhintegral(4*arctanh(a*x))+2*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1+-8//3*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1+-2//3*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-2+-1//3*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-3)
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x)^-5, x) == :(1//3*a^-1*coshintegral(2*arctanh(a*x))+4//3*a^-1*coshintegral(4*arctanh(a*x))+x*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1+(1/2)*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-2+-8//3*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1+-2//3*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-2+-1//3*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-3+-1//4*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-4)
@test integrate((1+-1*a^2*x^2)^-3*arctanh(a*x)^-6, x) == :(2//15*a^-1*sinhintegral(2*arctanh(a*x))+16//15*a^-1*sinhintegral(4*arctanh(a*x))+x*(5+-5*a^2*x^2)^-1*arctanh(a*x)^-2+-32//15*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1+-8//15*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-2+-4//15*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-3+-1//5*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-4+-1//5*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-5+1//5*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-3+8//5*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1+1//5*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^-1*(1+a^2*x^2))
@test integrate((1+-1*a^2*x^2)^-4*arctanh(a*x), x) == :(-5//32*a^-1*(1+-1*a^2*x^2)^-1+-5//96*a^-1*(1+-1*a^2*x^2)^-2+-1//36*a^-1*(1+-1*a^2*x^2)^-3+5//32*a^-1*arctanh(a*x)^2+5*x*(16+-16*a^2*x^2)^-1*arctanh(a*x)+1//6*x*(1+-1*a^2*x^2)^-3*arctanh(a*x)+5//24*x*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-4*arctanh(a*x)^2, x) == :(245*x*(1152+-1152*a^2*x^2)^-1+1//108*x*(1+-1*a^2*x^2)^-3+5//48*a^-1*arctanh(a*x)^3+65//1728*x*(1+-1*a^2*x^2)^-2+245//1152*a^-1*arctanh(a*x)+5*x*(16+-16*a^2*x^2)^-1*arctanh(a*x)^2+-5//16*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)+-5//48*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)+-1//18*a^-1*(1+-1*a^2*x^2)^-3*arctanh(a*x)+1//6*x*(1+-1*a^2*x^2)^-3*arctanh(a*x)^2+5//24*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2)
@test integrate((1+-1*a^2*x^2)^-4*arctanh(a*x)^3, x) == :(-245//768*a^-1*(1+-1*a^2*x^2)^-1+-65//2304*a^-1*(1+-1*a^2*x^2)^-2+-1//216*a^-1*(1+-1*a^2*x^2)^-3+5//64*a^-1*arctanh(a*x)^4+245//768*a^-1*arctanh(a*x)^2+5*x*(16+-16*a^2*x^2)^-1*arctanh(a*x)^3+245*x*(384+-384*a^2*x^2)^-1*arctanh(a*x)+-15//32*a^-1*(1+-1*a^2*x^2)^-1*arctanh(a*x)^2+-5//32*a^-1*(1+-1*a^2*x^2)^-2*arctanh(a*x)^2+-1//12*a^-1*(1+-1*a^2*x^2)^-3*arctanh(a*x)^2+1//6*x*(1+-1*a^2*x^2)^-3*arctanh(a*x)^3+1//36*x*(1+-1*a^2*x^2)^-3*arctanh(a*x)+5//24*x*(1+-1*a^2*x^2)^-2*arctanh(a*x)^3+65//576*x*(1+-1*a^2*x^2)^-2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-4*arctanh(a*x)^(1/2), x) == :(5//24*a^-1*arctanh(a*x)^3//2+-3//512*pi^(1/2)*a^-1*erfi(2*arctanh(a*x)^(1/2))+1//192*a^-1*arctanh(a*x)^(1/2)*sinh(6*arctanh(a*x))+3//64*a^-1*arctanh(a*x)^(1/2)*sinh(4*arctanh(a*x))+3//512*pi^(1/2)*a^-1*erf(2*arctanh(a*x)^(1/2))+15//64*a^-1*arctanh(a*x)^(1/2)*sinh(2*arctanh(a*x))+-15//512*2^(1/2)*pi^(1/2)*a^-1*erfi(2^(1/2)*arctanh(a*x)^(1/2))+-1//4608*6^(1/2)*pi^(1/2)*a^-1*erfi(6^(1/2)*arctanh(a*x)^(1/2))+1//4608*6^(1/2)*pi^(1/2)*a^-1*erf(6^(1/2)*arctanh(a*x)^(1/2))+15//512*2^(1/2)*pi^(1/2)*a^-1*erf(2^(1/2)*arctanh(a*x)^(1/2)))
@test integrate(x^6*(1+-1*a^2*x^2)^-4*arctanh(a*x)^-1, x) == :(-5//16*a^-7*log(arctanh(a*x))+-3//16*a^-7*coshintegral(4*arctanh(a*x))+1//32*a^-7*coshintegral(6*arctanh(a*x))+15//32*a^-7*coshintegral(2*arctanh(a*x)))
@test integrate(x^5*(1+-1*a^2*x^2)^-4*arctanh(a*x)^-1, x) == :(-1//8*a^-6*sinhintegral(4*arctanh(a*x))+1//32*a^-6*sinhintegral(6*arctanh(a*x))+5//32*a^-6*sinhintegral(2*arctanh(a*x)))
@test integrate(x^4*(1+-1*a^2*x^2)^-4*arctanh(a*x)^-1, x) == :(-1//16*a^-5*coshintegral(4*arctanh(a*x))+-1//32*a^-5*coshintegral(2*arctanh(a*x))+1//16*a^-5*log(arctanh(a*x))+1//32*a^-5*coshintegral(6*arctanh(a*x)))
@test integrate(x^3*(1+-1*a^2*x^2)^-4*arctanh(a*x)^-1, x) == :(-3//32*a^-4*sinhintegral(2*arctanh(a*x))+1//32*a^-4*sinhintegral(6*arctanh(a*x)))
@test integrate(x^2*(1+-1*a^2*x^2)^-4*arctanh(a*x)^-1, x) == :(-1//16*a^-3*log(arctanh(a*x))+-1//32*a^-3*coshintegral(2*arctanh(a*x))+1//16*a^-3*coshintegral(4*arctanh(a*x))+1//32*a^-3*coshintegral(6*arctanh(a*x)))
@test integrate(x*(1+-1*a^2*x^2)^-4*arctanh(a*x)^-1, x) == :(1//8*a^-2*sinhintegral(4*arctanh(a*x))+1//32*a^-2*sinhintegral(6*arctanh(a*x))+5//32*a^-2*sinhintegral(2*arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-4*arctanh(a*x)^-1, x) == :(1//32*a^-1*coshintegral(6*arctanh(a*x))+3//16*a^-1*coshintegral(4*arctanh(a*x))+5//16*a^-1*log(arctanh(a*x))+15//32*a^-1*coshintegral(2*arctanh(a*x)))
@test integrate(x*(1+-1*a^2*x^2)^-4*arctanh(a*x)^-2, x) == :((1/2)*a^-2*coshintegral(4*arctanh(a*x))+3//16*a^-2*coshintegral(6*arctanh(a*x))+5//16*a^-2*coshintegral(2*arctanh(a*x))+-1*x*a^-1*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-1)
@test integrate((1+-1*a^2*x^2)^-4*arctanh(a*x)^-2, x) == :(3//4*a^-1*sinhintegral(4*arctanh(a*x))+3//16*a^-1*sinhintegral(6*arctanh(a*x))+15//16*a^-1*sinhintegral(2*arctanh(a*x))+-1*a^-1*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-1)
@test integrate(x*(1+-1*a^2*x^2)^-4*arctanh(a*x)^-3, x) == :(a^-2*sinhintegral(4*arctanh(a*x))+5//16*a^-2*sinhintegral(2*arctanh(a*x))+9//16*a^-2*sinhintegral(6*arctanh(a*x))+-3*a^-2*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-1+5//2*a^-2*(1+-1*a^2*x^2)^-2*arctanh(a*x)^-1+-1//2*x*a^-1*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-4*arctanh(a*x)^-3, x) == :(3//2*a^-1*coshintegral(4*arctanh(a*x))+9//16*a^-1*coshintegral(6*arctanh(a*x))+15//16*a^-1*coshintegral(2*arctanh(a*x))+-3*x*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-1+-1//2*a^-1*(1+-1*a^2*x^2)^-3*arctanh(a*x)^-2)
@test integrate(x^5*(1+-1*a^2*x^2)^-1//2*arctanh(a*x), x) == :(89//120*a^-6*arcsin(a*x)+-8//15*a^-6*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-5//24*x*a^-5*(1+-1*a^2*x^2)^(1/2)+-1//20*a^-3*x^3*(1+-1*a^2*x^2)^(1/2)+-4//15*a^-4*x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//5*a^-2*x^4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^4*(1+-1*a^2*x^2)^-1//2*arctanh(a*x), x) == :(-5//8*a^-5*(1+-1*a^2*x^2)^(1/2)+1//12*a^-5*(1+-1*a^2*x^2)^3//2+-3//4*a^-5*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-3//8*im*a^-5*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3//8*im*a^-5*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-3//8*x*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//4*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x), x) == :(5//6*a^-4*arcsin(a*x)+-2//3*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//6*x*a^-3*(1+-1*a^2*x^2)^(1/2)+-1//3*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x), x) == :(-1//2*a^-3*(1+-1*a^2*x^2)^(1/2)+(1/2)*im*a^-3*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*a^-3*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-1//2*im*a^-3*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//2*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x), x) == :(a^-2*arcsin(a*x)+-1*a^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-1//2*arctanh(a*x), x) == :(im*a^-1*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*im*a^-1*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-2*a^-1*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x), x) == :(-1*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x), x) == :(-1*a*arctanh((1+-1*a^2*x^2)^(1/2))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x), x) == :((1/2)*a^2*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//2*a^2*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*a^2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//2*a*x^-1*(1+-1*a^2*x^2)^(1/2)+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2, x) == :(-1//3*a^-4*(1+-1*a^2*x^2)^(1/2)+-10//3*a^-4*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-5//3*im*a^-4*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-2//3*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+5//3*im*a^-4*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//3*x*a^-3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//3*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2)
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2, x) == :(a^-3*arcsin(a*x)+im*a^-3*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+a^-3*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+-1*im*a^-3*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+-1*a^-3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+im*a^-3*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x)+-1*im*a^-3*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x)+-1//2*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2)
@test integrate(x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2, x) == :(-1*a^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-4*a^-2*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-2*im*a^-2*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+2*im*a^-2*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate((1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2, x) == :(-2*im*a^-1*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+2*im*a^-1*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+2*a^-1*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+-2*im*a^-1*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x)+2*im*a^-1*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2, x) == :(-2*Polylogarithms.polylog(3,exp(arctanh(a*x)))+2*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))+-2*arctanh(a*x)^2*arctanh(exp(arctanh(a*x)))+-2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))*arctanh(a*x)+2*Polylogarithms.polylog(2,exp(arctanh(a*x)))*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2, x) == :(-2*a*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+2*a*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-4*a*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2, x) == :(a^2*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))+-1*a^2*Polylogarithms.polylog(3,exp(arctanh(a*x)))+-1*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+a^2*Polylogarithms.polylog(2,exp(arctanh(a*x)))*arctanh(a*x)+-1*a^2*arctanh(a*x)^2*arctanh(exp(arctanh(a*x)))+-1*a^2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))*arctanh(a*x)+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-1*a*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3, x) == :(a^-4*arcsin(a*x)+-1*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-5*im*a^-4*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+5*im*a^-4*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+5*a^-4*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+-2//3*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3+-5*im*a^-4*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x)+5*im*a^-4*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x)+-1//2*x*a^-3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-1//3*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3)
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3, x) == :(a^-3*arctanh(a*x)^3*arctan(exp(arctanh(a*x)))+-6*a^-3*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-3*im*a^-3*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-3*im*a^-3*Polylogarithms.polylog(4,-1*im*exp(arctanh(a*x)))+3*im*a^-3*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3*im*a^-3*Polylogarithms.polylog(4,im*exp(arctanh(a*x)))+-3//2*a^-3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-3*im*a^-3*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))*arctanh(a*x)+3*im*a^-3*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))*arctanh(a*x)+-3//2*im*a^-3*arctanh(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))+-1//2*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3+3//2*im*a^-3*arctanh(a*x)^2*Polylogarithms.polylog(2,im*exp(arctanh(a*x))))
@test integrate(x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3, x) == :(-1*a^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3+-6*im*a^-2*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+6*im*a^-2*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+6*a^-2*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+-6*im*a^-2*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x)+6*im*a^-2*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3, x) == :(-6*im*a^-1*Polylogarithms.polylog(4,-1*im*exp(arctanh(a*x)))+2*a^-1*arctanh(a*x)^3*arctan(exp(arctanh(a*x)))+6*im*a^-1*Polylogarithms.polylog(4,im*exp(arctanh(a*x)))+-6*im*a^-1*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))*arctanh(a*x)+-3*im*a^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))+3*im*a^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))+6*im*a^-1*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3, x) == :(-6*Polylogarithms.polylog(4,-1*exp(arctanh(a*x)))+6*Polylogarithms.polylog(4,exp(arctanh(a*x)))+-6*Polylogarithms.polylog(3,exp(arctanh(a*x)))*arctanh(a*x)+-3*arctanh(a*x)^2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))+-2*arctanh(a*x)^3*arctanh(exp(arctanh(a*x)))+3*arctanh(a*x)^2*Polylogarithms.polylog(2,exp(arctanh(a*x)))+6*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3, x) == :(-6*a*Polylogarithms.polylog(3,exp(arctanh(a*x)))+6*a*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3+-6*a*arctanh(a*x)^2*arctanh(exp(arctanh(a*x)))+-6*a*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))*arctanh(a*x)+6*a*Polylogarithms.polylog(2,exp(arctanh(a*x)))*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3, x) == :(-3*a^2*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-3*a^2*Polylogarithms.polylog(4,-1*exp(arctanh(a*x)))+3*a^2*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3*a^2*Polylogarithms.polylog(4,exp(arctanh(a*x)))+-1*a^2*arctanh(a*x)^3*arctanh(exp(arctanh(a*x)))+-6*a^2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-3*a^2*Polylogarithms.polylog(3,exp(arctanh(a*x)))*arctanh(a*x)+3*a^2*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))*arctanh(a*x)+-3//2*a^2*arctanh(a*x)^2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3+3//2*a^2*arctanh(a*x)^2*Polylogarithms.polylog(2,exp(arctanh(a*x)))+-3//2*a*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2)
@test integrate(x^3*(1+-1*a^2*x^2)^-3//2*arctanh(a*x), x) == :(-1*a^-4*arcsin(a*x)+a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+a^-4*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-1*x*a^-3*(1+-1*a^2*x^2)^-1//2)
@test integrate(x^2*(1+-1*a^2*x^2)^-3//2*arctanh(a*x), x) == :(-1*a^-3*(1+-1*a^2*x^2)^-1//2+im*a^-3*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*im*a^-3*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+2*a^-3*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+x*a^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x), x) == :(a^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-1*x*a^-1*(1+-1*a^2*x^2)^-1//2)
@test integrate((1+-1*a^2*x^2)^-3//2*arctanh(a*x), x) == :(-1*a^-1*(1+-1*a^2*x^2)^-1//2+x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x), x) == :(-1*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*a*x*(1+-1*a^2*x^2)^-1//2+Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate(x^-2*(1+-1*a^2*x^2)^-3//2*arctanh(a*x), x) == :(-1*a*(1+-1*a^2*x^2)^-1//2+-1*a*arctanh((1+-1*a^2*x^2)^(1/2))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+x*a^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-3//2*arctanh(a*x), x) == :(-3//2*a^2*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3//2*a^2*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+a^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-1*x*a^3*(1+-1*a^2*x^2)^-1//2+-3*a^2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//2*a*x^-1*(1+-1*a^2*x^2)^(1/2)+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2, x) == :(2*a^-4*(1+-1*a^2*x^2)^-1//2+a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+a^-4*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-2*im*a^-4*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+2*im*a^-4*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+4*a^-4*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-2*x*a^-3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2, x) == :(-2*im*a^-3*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+-2*a^-3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-2*a^-3*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+2*im*a^-3*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+2*x*a^-2*(1+-1*a^2*x^2)^-1//2+x*a^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-2*im*a^-3*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x)+2*im*a^-3*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2, x) == :(2*a^-2*(1+-1*a^2*x^2)^-1//2+a^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-2*x*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2, x) == :(2*x*(1+-1*a^2*x^2)^-1//2+x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-2*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2, x) == :(-2*Polylogarithms.polylog(3,exp(arctanh(a*x)))+2*(1+-1*a^2*x^2)^-1//2+2*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))+(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-2*arctanh(a*x)^2*arctanh(exp(arctanh(a*x)))+-2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))*arctanh(a*x)+2*Polylogarithms.polylog(2,exp(arctanh(a*x)))*arctanh(a*x)+-2*a*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2, x) == :(-2*a*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+2*a*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-4*a*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-2*a*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+2*x*a^2*(1+-1*a^2*x^2)^-1//2+x*a^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2)
@test integrate(x^-3*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2, x) == :(-1*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+-3*a^2*Polylogarithms.polylog(3,exp(arctanh(a*x)))+2*a^2*(1+-1*a^2*x^2)^-1//2+3*a^2*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))+a^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-3*a^2*arctanh(a*x)^2*arctanh(exp(arctanh(a*x)))+-3*a^2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))*arctanh(a*x)+3*a^2*Polylogarithms.polylog(2,exp(arctanh(a*x)))*arctanh(a*x)+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-1*a*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-2*x*a^3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3, x) == :(a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3+a^-4*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+-6*im*a^-4*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+-6*x*a^-3*(1+-1*a^2*x^2)^-1//2+-6*a^-4*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+6*im*a^-4*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+6*a^-4*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-6*im*a^-4*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x)+-3*x*a^-3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+6*im*a^-4*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3, x) == :(-6*a^-3*(1+-1*a^2*x^2)^-1//2+-6*im*a^-3*Polylogarithms.polylog(4,im*exp(arctanh(a*x)))+-3*a^-3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-2*a^-3*arctanh(a*x)^3*arctan(exp(arctanh(a*x)))+6*im*a^-3*Polylogarithms.polylog(4,-1*im*exp(arctanh(a*x)))+x*a^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+-6*im*a^-3*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))*arctanh(a*x)+-3*im*a^-3*arctanh(a*x)^2*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))+3*im*a^-3*arctanh(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))+6*im*a^-3*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))*arctanh(a*x)+6*x*a^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3, x) == :(a^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+-6*x*a^-1*(1+-1*a^2*x^2)^-1//2+6*a^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-3*x*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2)
@test integrate((1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3, x) == :(-6*a^-1*(1+-1*a^2*x^2)^-1//2+x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+-3*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+6*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3, x) == :(-6*Polylogarithms.polylog(4,-1*exp(arctanh(a*x)))+6*Polylogarithms.polylog(4,exp(arctanh(a*x)))+(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+-6*Polylogarithms.polylog(3,exp(arctanh(a*x)))*arctanh(a*x)+-3*arctanh(a*x)^2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))+-2*arctanh(a*x)^3*arctanh(exp(arctanh(a*x)))+3*arctanh(a*x)^2*Polylogarithms.polylog(2,exp(arctanh(a*x)))+6*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+6*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))*arctanh(a*x)+-6*a*x*(1+-1*a^2*x^2)^-1//2+-3*a*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2)
@test integrate(x^-2*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3, x) == :(-6*a*(1+-1*a^2*x^2)^-1//2+-6*a*Polylogarithms.polylog(3,exp(arctanh(a*x)))+6*a*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3+-6*a*arctanh(a*x)^2*arctanh(exp(arctanh(a*x)))+-6*a*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))*arctanh(a*x)+-3*a*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+6*a*Polylogarithms.polylog(2,exp(arctanh(a*x)))*arctanh(a*x)+x*a^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+6*x*a^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3, x) == :(-9*a^2*Polylogarithms.polylog(4,-1*exp(arctanh(a*x)))+-3*a^2*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3*a^2*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+9*a^2*Polylogarithms.polylog(4,exp(arctanh(a*x)))+a^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+-9*a^2*Polylogarithms.polylog(3,exp(arctanh(a*x)))*arctanh(a*x)+-6*x*a^3*(1+-1*a^2*x^2)^-1//2+-6*a^2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-3*a^2*arctanh(a*x)^3*arctanh(exp(arctanh(a*x)))+6*a^2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+9*a^2*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))*arctanh(a*x)+-9//2*a^2*arctanh(a*x)^2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3+9//2*a^2*arctanh(a*x)^2*Polylogarithms.polylog(2,exp(arctanh(a*x)))+-3*x*a^3*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-3//2*a*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2)
@test integrate(x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-1, x) == :(a^-2*sinhintegral(arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-1, x) == :(a^-1*coshintegral(arctanh(a*x)))
@test integrate(x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-2, x) == :(a^-2*coshintegral(arctanh(a*x))+-1*x*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^-1)
@test integrate((1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-2, x) == :(a^-1*sinhintegral(arctanh(a*x))+-1*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^-1)
@test integrate(x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-3, x) == :((1/2)*a^-2*sinhintegral(arctanh(a*x))+-1//2*a^-2*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^-1+-1//2*x*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-3, x) == :((1/2)*a^-1*coshintegral(arctanh(a*x))+-1//2*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^-1+-1//2*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^-2)
@test integrate(x^4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(-7//72*a^-5*(1+-1*a^2*x^2)^3//2+1//16*a^-5*(1+-1*a^2*x^2)^(1/2)+1//30*a^-5*(1+-1*a^2*x^2)^5//2+-1//8*a^-5*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-1//16*im*a^-5*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//6*x^5*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+1//16*im*a^-5*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//16*x*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//24*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(11//120*a^-4*arcsin(a*x)+-2//15*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+1//5*x^4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+1//20*a^-1*x^3*(1+-1*a^2*x^2)^(1/2)+1//24*x*a^-3*(1+-1*a^2*x^2)^(1/2)+-1//15*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(-1//12*a^-3*(1+-1*a^2*x^2)^3//2+1//8*a^-3*(1+-1*a^2*x^2)^(1/2)+-1//4*a^-3*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-1//8*im*a^-3*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//4*x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+1//8*im*a^-3*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//8*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(1//6*a^-2*arcsin(a*x)+-1//3*a^-2*(1+-1*a^2*x^2)^3//2*arctanh(a*x)+1//6*x*a^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :((1/2)*a^-1*(1+-1*a^2*x^2)^(1/2)+(1/2)*im*a^-1*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+(1/2)*x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1*a^-1*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-1//2*im*a^-1*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate(x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(-1*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*arcsin(a*x)+(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate(x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(-1*a*arctanh((1+-1*a^2*x^2)^(1/2))+im*a*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*im*a*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+2*a*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :((1/2)*a^2*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//2*a^2*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+a^2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//2*a*x^-1*(1+-1*a^2*x^2)^(1/2)+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(1//6*a^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*x^-3*(1+-1*a^2*x^2)^3//2*arctanh(a*x)+-1//6*a*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-5*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(-1//8*a^4*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//8*a^4*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//4*x^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//12*a*x^-3*(1+-1*a^2*x^2)^(1/2)+-1//24*a^3*x^-1*(1+-1*a^2*x^2)^(1/2)+1//4*a^4*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//8*a^2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-6*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(11//120*a^5*arctanh((1+-1*a^2*x^2)^(1/2))+-1//5*x^-5*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//20*a*x^-4*(1+-1*a^2*x^2)^(1/2)+-1//24*a^3*x^-2*(1+-1*a^2*x^2)^(1/2)+1//15*a^2*x^-3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+2//15*a^4*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-7*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :(-1//16*a^6*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//16*a^6*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-11//360*a^3*x^-3*(1+-1*a^2*x^2)^(1/2)+-1//6*x^-6*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//30*a*x^-5*(1+-1*a^2*x^2)^(1/2)+1//8*a^6*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//720*a^5*x^-1*(1+-1*a^2*x^2)^(1/2)+1//16*a^4*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+1//24*a^2*x^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(-19//360*a^-5*arcsin(a*x)+-1//8*im*a^-5*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+-1//360*a^-5*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+1//6*x^5*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+1//8*im*a^-5*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+1//8*a^-5*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+1//18*x*a^-4*(1+-1*a^2*x^2)^(1/2)+1//60*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)+-1//8*im*a^-5*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x)+-1//16*x*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-1//24*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+1//8*im*a^-5*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x)+1//15*a^-1*x^4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+11//180*a^-3*x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(-1//30*a^-4*(1+-1*a^2*x^2)^3//2+11//60*a^-4*(1+-1*a^2*x^2)^(1/2)+-11//30*a^-4*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-11//60*im*a^-4*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-2//15*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+1//5*x^4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+11//60*im*a^-4*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//15*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+1//10*a^-1*x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+1//12*x*a^-3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(-1//6*a^-3*arcsin(a*x)+-1//4*im*a^-3*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+1//4*im*a^-3*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+1//4*a^-3*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+1//4*x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+1//12*x*a^-2*(1+-1*a^2*x^2)^(1/2)+1//12*a^-3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//4*im*a^-3*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x)+-1//8*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+1//4*im*a^-3*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x)+1//6*a^-1*x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(1//3*a^-2*(1+-1*a^2*x^2)^(1/2)+-2//3*a^-2*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-1//3*im*a^-2*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//3*a^-2*(1+-1*a^2*x^2)^3//2*arctanh(a*x)^2+1//3*im*a^-2*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//3*x*a^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(-1*a^-1*arcsin(a*x)+im*a^-1*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+a^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+a^-1*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+(1/2)*x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-1*im*a^-1*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+im*a^-1*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x)+-1*im*a^-1*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(-2*Polylogarithms.polylog(3,exp(arctanh(a*x)))+2*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))+(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-2*im*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-2*arctanh(a*x)^2*arctanh(exp(arctanh(a*x)))+-2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))*arctanh(a*x)+2*im*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+2*Polylogarithms.polylog(2,exp(arctanh(a*x)))*arctanh(a*x)+4*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(-2*a*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+2*a*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-4*a*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-2*im*a*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+-2*a*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+2*im*a*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+-2*im*a*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x)+2*im*a*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(a^2*Polylogarithms.polylog(3,exp(arctanh(a*x)))+-1*a^2*Polylogarithms.polylog(3,-1*exp(arctanh(a*x)))+-1*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+a^2*arctanh(a*x)^2*arctanh(exp(arctanh(a*x)))+a^2*Polylogarithms.polylog(2,-1*exp(arctanh(a*x)))*arctanh(a*x)+-1*a^2*Polylogarithms.polylog(2,exp(arctanh(a*x)))*arctanh(a*x)+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-1*a*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(-1//3*a^3*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//3*a^3*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//3*a^2*x^-1*(1+-1*a^2*x^2)^(1/2)+-1//3*x^-3*(1+-1*a^2*x^2)^3//2*arctanh(a*x)^2+2//3*a^3*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//3*a*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^4*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(-3//80*a^-5*(1+-1*a^2*x^2)^5//2+1//56*a^-5*(1+-1*a^2*x^2)^7//2+1//192*a^-5*(1+-1*a^2*x^2)^3//2+3//128*a^-5*(1+-1*a^2*x^2)^(1/2)+-3//64*a^-5*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-3//128*im*a^-5*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3//16*x^5*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+3//128*im*a^-5*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-3//128*x*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//8*a^2*x^7*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//64*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(17//560*a^-4*arcsin(a*x)+-2//35*a^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//42*a*x^5*(1+-1*a^2*x^2)^(1/2)+3//112*x*a^-3*(1+-1*a^2*x^2)^(1/2)+8//35*x^4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+23//840*a^-1*x^3*(1+-1*a^2*x^2)^(1/2)+-1//7*a^2*x^6*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//35*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(-1//30*a^-3*(1+-1*a^2*x^2)^5//2+1//16*a^-3*(1+-1*a^2*x^2)^(1/2)+1//72*a^-3*(1+-1*a^2*x^2)^3//2+-1//8*a^-3*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-1//16*im*a^-3*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//16*im*a^-3*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+7//24*x^3*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//6*a^2*x^5*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//16*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(3//40*a^-2*arcsin(a*x)+-1//5*a^-2*(1+-1*a^2*x^2)^5//2*arctanh(a*x)+1//20*x*a^-1*(1+-1*a^2*x^2)^3//2+3//40*x*a^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(1//12*a^-1*(1+-1*a^2*x^2)^3//2+3//8*a^-1*(1+-1*a^2*x^2)^(1/2)+-3//4*a^-1*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-3//8*im*a^-1*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//4*x*(1+-1*a^2*x^2)^3//2*arctanh(a*x)+3//8*im*a^-1*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3//8*x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(-1*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-7//6*arcsin(a*x)+(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//3*(1+-1*a^2*x^2)^3//2*arctanh(a*x)+-1//6*a*x*(1+-1*a^2*x^2)^(1/2)+Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate(x^-2*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(-1*a*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*a*(1+-1*a^2*x^2)^(1/2)+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+3*a*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-3//2*im*a*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3//2*im*a*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//2*x*a^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(a^2*arcsin(a*x)+-3//2*a^2*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3//2*a^2*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*a^2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+3*a^2*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//2*a*x^-1*(1+-1*a^2*x^2)^(1/2)+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-4*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(7//6*a^3*arctanh((1+-1*a^2*x^2)^(1/2))+im*a^3*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*im*a^3*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-2*a^3*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-1//3*x^-3*(1+-1*a^2*x^2)^3//2*arctanh(a*x)+-1//6*a*x^-2*(1+-1*a^2*x^2)^(1/2)+a^2*x^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-5*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(-3//8*a^4*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3//8*a^4*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-3//4*a^4*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//4*x^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//12*a*x^-3*(1+-1*a^2*x^2)^(1/2)+11//24*a^3*x^-1*(1+-1*a^2*x^2)^(1/2)+5//8*a^2*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate(x^-6*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(-3//40*a^5*arctanh((1+-1*a^2*x^2)^(1/2))+-1//5*x^-5*(1+-1*a^2*x^2)^5//2*arctanh(a*x)+-1//20*a*x^-4*(1+-1*a^2*x^2)^3//2+3//40*a^3*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-7*(1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(-1//16*a^6*Polylogarithms.polylog(2,(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//16*a^6*Polylogarithms.polylog(2,-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//6*x^-6*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1//8*a^6*arctanh(a*x)*arctanh((1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1//30*a*x^-5*(1+-1*a^2*x^2)^(1/2)+19//360*a^3*x^-3*(1+-1*a^2*x^2)^(1/2)+31//720*a^5*x^-1*(1+-1*a^2*x^2)^(1/2)+-1//16*a^4*x^-2*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+7//24*a^2*x^-4*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^5//2*arctanh(a*x), x) == :(1//30*a^-1*(1+-1*a^2*x^2)^5//2+5//16*a^-1*(1+-1*a^2*x^2)^(1/2)+5//72*a^-1*(1+-1*a^2*x^2)^3//2+-5//8*a^-1*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-5//16*im*a^-1*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//6*x*(1+-1*a^2*x^2)^5//2*arctanh(a*x)+5//16*im*a^-1*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+5//16*x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+5//24*x*(1+-1*a^2*x^2)^3//2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^3//2*arctanh(a*x), x) == :(1//12*a^-1*(1+-1*a^2*x^2)^3//2+3//8*a^-1*(1+-1*a^2*x^2)^(1/2)+-3//4*a^-1*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-3//8*im*a^-1*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+1//4*x*(1+-1*a^2*x^2)^3//2*arctanh(a*x)+3//8*im*a^-1*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3//8*x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^(1/2)*arctanh(a*x), x) == :((1/2)*a^-1*(1+-1*a^2*x^2)^(1/2)+(1/2)*im*a^-1*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+(1/2)*x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+-1*a^-1*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-1//2*im*a^-1*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate((1+-1*a^2*x^2)^-5//2*arctanh(a*x), x) == :(-2//3*a^-1*(1+-1*a^2*x^2)^-1//2+-1//9*a^-1*(1+-1*a^2*x^2)^-3//2+1//3*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)+2//3*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-7//2*arctanh(a*x), x) == :(-8//15*a^-1*(1+-1*a^2*x^2)^-1//2+-4//45*a^-1*(1+-1*a^2*x^2)^-3//2+-1//25*a^-1*(1+-1*a^2*x^2)^-5//2+1//5*x*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)+4//15*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)+8//15*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-9//2*arctanh(a*x), x) == :(-16//35*a^-1*(1+-1*a^2*x^2)^-1//2+-8//105*a^-1*(1+-1*a^2*x^2)^-3//2+-6//175*a^-1*(1+-1*a^2*x^2)^-5//2+-1//49*a^-1*(1+-1*a^2*x^2)^-7//2+1//7*x*(1+-1*a^2*x^2)^-7//2*arctanh(a*x)+6//35*x*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)+8//35*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)+16//35*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^3//2*arctanh(a*x), x) == :(1//12*a^-1*(c+-1*c*a^2*x^2)^3//2+1//4*x*(c+-1*c*a^2*x^2)^3//2*arctanh(a*x)+3//8*c*a^-1*(c+-1*c*a^2*x^2)^(1/2)+3//8*c*x*(c+-1*c*a^2*x^2)^(1/2)*arctanh(a*x)+-3//4*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-3//8*im*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3//8*im*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*arctanh(a*x), x) == :((1/2)*a^-1*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*x*(c+-1*c*a^2*x^2)^(1/2)*arctanh(a*x)+(1/2)*im*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+-1//2*im*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^-1//2*arctanh(a*x), x) == :(im*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-1*im*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-2*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*arctanh(a*x), x) == :(-1*a^-1*c^-1*(c+-1*c*a^2*x^2)^-1//2+x*c^-1*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-5//2*arctanh(a*x), x) == :(-2//3*a^-1*c^-2*(c+-1*c*a^2*x^2)^-1//2+-1//9*a^-1*c^-1*(c+-1*c*a^2*x^2)^-3//2+1//3*x*c^-1*(c+-1*c*a^2*x^2)^-3//2*arctanh(a*x)+2//3*x*c^-2*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*arctanh(a*x), x) == :(-8//15*a^-1*c^-3*(c+-1*c*a^2*x^2)^-1//2+-4//45*a^-1*c^-2*(c+-1*c*a^2*x^2)^-3//2+-1//25*a^-1*c^-1*(c+-1*c*a^2*x^2)^-5//2+1//5*x*c^-1*(c+-1*c*a^2*x^2)^-5//2*arctanh(a*x)+4//15*x*c^-2*(c+-1*c*a^2*x^2)^-3//2*arctanh(a*x)+8//15*x*c^-3*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2, x) == :(-1*a^-1*arcsin(a*x)+im*a^-1*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))+a^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)+a^-1*arctanh(a*x)^2*arctan(exp(arctanh(a*x)))+(1/2)*x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-1*im*a^-1*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))+im*a^-1*Polylogarithms.polylog(2,im*exp(arctanh(a*x)))*arctanh(a*x)+-1*im*a^-1*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-5//2*arctanh(a*x)^2, x) == :(2//27*x*(1+-1*a^2*x^2)^-3//2+40//27*x*(1+-1*a^2*x^2)^-1//2+-4//3*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-2//9*a^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)+1//3*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2+2//3*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2)
@test integrate((1+-1*a^2*x^2)^-7//2*arctanh(a*x)^2, x) == :(2//125*x*(1+-1*a^2*x^2)^-5//2+272//3375*x*(1+-1*a^2*x^2)^-3//2+4144//3375*x*(1+-1*a^2*x^2)^-1//2+-16//15*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-8//45*a^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)+-2//25*a^-1*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)+1//5*x*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)^2+4//15*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2+8//15*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2)
@test integrate((1+-1*a^2*x^2)^-9//2*arctanh(a*x)^2, x) == :(2//343*x*(1+-1*a^2*x^2)^-7//2+888//42875*x*(1+-1*a^2*x^2)^-5//2+30256//385875*x*(1+-1*a^2*x^2)^-3//2+413312//385875*x*(1+-1*a^2*x^2)^-1//2+-32//35*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)+-16//105*a^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)+-12//175*a^-1*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)+-2//49*a^-1*(1+-1*a^2*x^2)^-7//2*arctanh(a*x)+1//7*x*(1+-1*a^2*x^2)^-7//2*arctanh(a*x)^2+6//35*x*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)^2+8//35*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2+16//35*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2)
@test integrate((1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3, x) == :(a^-1*arctanh(a*x)^3*arctan(exp(arctanh(a*x)))+(1/2)*x*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^3+-3*im*a^-1*Polylogarithms.polylog(2,im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+-3*im*a^-1*Polylogarithms.polylog(4,-1*im*exp(arctanh(a*x)))+3*im*a^-1*Polylogarithms.polylog(2,-1*im*(1+a*x)^-1//2*(1+-1*a*x)^(1/2))+3*im*a^-1*Polylogarithms.polylog(4,im*exp(arctanh(a*x)))+6*a^-1*arctan((1+a*x)^-1//2*(1+-1*a*x)^(1/2))*arctanh(a*x)+3//2*a^-1*(1+-1*a^2*x^2)^(1/2)*arctanh(a*x)^2+-3*im*a^-1*Polylogarithms.polylog(3,im*exp(arctanh(a*x)))*arctanh(a*x)+3*im*a^-1*Polylogarithms.polylog(3,-1*im*exp(arctanh(a*x)))*arctanh(a*x)+-3//2*im*a^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(arctanh(a*x)))+3//2*im*a^-1*arctanh(a*x)^2*Polylogarithms.polylog(2,im*exp(arctanh(a*x))))
@test integrate((1+-1*a^2*x^2)^-5//2*arctanh(a*x)^3, x) == :(-40//9*a^-1*(1+-1*a^2*x^2)^-1//2+-2//27*a^-1*(1+-1*a^2*x^2)^-3//2+-2*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-1//3*a^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2+1//3*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3+2//3*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+2//9*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)+40//9*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-7//2*arctanh(a*x)^3, x) == :(-4144//1125*a^-1*(1+-1*a^2*x^2)^-1//2+-272//3375*a^-1*(1+-1*a^2*x^2)^-3//2+-6//625*a^-1*(1+-1*a^2*x^2)^-5//2+-8//5*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-4//15*a^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2+-3//25*a^-1*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)^2+1//5*x*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)^3+4//15*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3+6//125*x*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)+8//15*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+272//1125*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)+4144//1125*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-9//2*arctanh(a*x)^3, x) == :(-413312//128625*a^-1*(1+-1*a^2*x^2)^-1//2+-30256//385875*a^-1*(1+-1*a^2*x^2)^-3//2+-2664//214375*a^-1*(1+-1*a^2*x^2)^-5//2+-6//2401*a^-1*(1+-1*a^2*x^2)^-7//2+-48//35*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^2+-18//175*a^-1*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)^2+-8//35*a^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^2+-3//49*a^-1*(1+-1*a^2*x^2)^-7//2*arctanh(a*x)^2+1//7*x*(1+-1*a^2*x^2)^-7//2*arctanh(a*x)^3+6//35*x*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)^3+6//343*x*(1+-1*a^2*x^2)^-7//2*arctanh(a*x)+8//35*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^3+16//35*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^3+2664//42875*x*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)+30256//128625*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)+413312//128625*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-1, x) == :(a^-1*coshintegral(arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-5//2*arctanh(a*x)^-1, x) == :(1//4*a^-1*coshintegral(3*arctanh(a*x))+3//4*a^-1*coshintegral(arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-7//2*arctanh(a*x)^-1, x) == :(1//16*a^-1*coshintegral(5*arctanh(a*x))+5//8*a^-1*coshintegral(arctanh(a*x))+5//16*a^-1*coshintegral(3*arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-9//2*arctanh(a*x)^-1, x) == :(1//64*a^-1*coshintegral(7*arctanh(a*x))+7//64*a^-1*coshintegral(5*arctanh(a*x))+21//64*a^-1*coshintegral(3*arctanh(a*x))+35//64*a^-1*coshintegral(arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-2, x) == :(a^-1*sinhintegral(arctanh(a*x))+-1*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^-1)
@test integrate((1+-1*a^2*x^2)^-5//2*arctanh(a*x)^-2, x) == :(3//4*a^-1*sinhintegral(3*arctanh(a*x))+3//4*a^-1*sinhintegral(arctanh(a*x))+-1*a^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-1)
@test integrate((1+-1*a^2*x^2)^-7//2*arctanh(a*x)^-2, x) == :(5//8*a^-1*sinhintegral(arctanh(a*x))+5//16*a^-1*sinhintegral(5*arctanh(a*x))+15//16*a^-1*sinhintegral(3*arctanh(a*x))+-1*a^-1*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)^-1)
@test integrate((1+-1*a^2*x^2)^-9//2*arctanh(a*x)^-2, x) == :(7//64*a^-1*sinhintegral(7*arctanh(a*x))+35//64*a^-1*sinhintegral(5*arctanh(a*x))+35//64*a^-1*sinhintegral(arctanh(a*x))+63//64*a^-1*sinhintegral(3*arctanh(a*x))+-1*a^-1*(1+-1*a^2*x^2)^-7//2*arctanh(a*x)^-1)
@test integrate((1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-3, x) == :((1/2)*a^-1*coshintegral(arctanh(a*x))+-1//2*x*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^-1+-1//2*a^-1*(1+-1*a^2*x^2)^-1//2*arctanh(a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-5//2*arctanh(a*x)^-3, x) == :(3//8*a^-1*coshintegral(arctanh(a*x))+9//8*a^-1*coshintegral(3*arctanh(a*x))+-3//2*x*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-1+-1//2*a^-1*(1+-1*a^2*x^2)^-3//2*arctanh(a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-7//2*arctanh(a*x)^-3, x) == :(5//16*a^-1*coshintegral(arctanh(a*x))+25//32*a^-1*coshintegral(5*arctanh(a*x))+45//32*a^-1*coshintegral(3*arctanh(a*x))+-5//2*x*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)^-1+-1//2*a^-1*(1+-1*a^2*x^2)^-5//2*arctanh(a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-9//2*arctanh(a*x)^-3, x) == :(35//128*a^-1*coshintegral(arctanh(a*x))+49//128*a^-1*coshintegral(7*arctanh(a*x))+175//128*a^-1*coshintegral(5*arctanh(a*x))+189//128*a^-1*coshintegral(3*arctanh(a*x))+-7//2*x*(1+-1*a^2*x^2)^-7//2*arctanh(a*x)^-1+-1//2*a^-1*(1+-1*a^2*x^2)^-7//2*arctanh(a*x)^-2)
@test integrate((1+-1*c^2*x^2)^-1*(a+b*arctanh(c*x))^2*(d+e*x), x) == :(e*c^-2*(a+b*arctanh(c*x))^2*log(2*(1+-1*c*x)^-1)+-1//2*e*b^2*c^-2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-1//3*e*b^-1*c^-2*(a+b*arctanh(c*x))^3+1//3*d*b^-1*c^-1*(a+b*arctanh(c*x))^3+b*e*c^-2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1))
@test integrate((c+d*x^2)^4*arctanh(a*x), x) == :(x*c^4*arctanh(a*x)+1//9*d^4*x^9*arctanh(a*x)+1//72*a^-1*d^4*x^8+1//630*a^-9*(35*d^4+315*a^8*c^4+180*c*a^2*d^3+378*a^4*c^2*d^2+420*d*a^6*c^3)*log(1+-1*a^2*x^2)+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+180*c*a^2*d^2+378*d*a^4*c^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*arctanh(a*x)+4//7*c*d^3*x^7*arctanh(a*x)+6//5*c^2*d^2*x^5*arctanh(a*x))
@test integrate((c+d*x^2)^3*arctanh(a*x), x) == :(x*c^3*arctanh(a*x)+1//7*d^3*x^7*arctanh(a*x)+1//42*a^-1*d^3*x^6+1//70*a^-7*(5*d^3+35*a^6*c^3+21*c*a^2*d^2+35*d*a^4*c^2)*log(1+-1*a^2*x^2)+d*c^2*x^3*arctanh(a*x)+1//70*d*a^-5*x^2*(5*d^2+35*a^4*c^2+21*c*d*a^2)+1//140*a^-3*d^2*x^4*(5d+21*c*a^2)+3//5*c*d^2*x^5*arctanh(a*x))
@test integrate((c+d*x^2)^2*arctanh(a*x), x) == :(x*c^2*arctanh(a*x)+1//5*d^2*x^5*arctanh(a*x)+1//20*a^-1*d^2*x^4+1//30*a^-5*(3*d^2+15*a^4*c^2+10*c*d*a^2)*log(1+-1*a^2*x^2)+1//30*d*a^-3*x^2*(3d+10*c*a^2)+2//3*c*d*x^3*arctanh(a*x))
@test integrate((c+d*x^2)*arctanh(a*x), x) == :(c*x*arctanh(a*x)+1//3*d*x^3*arctanh(a*x)+1//6*d*a^-1*x^2+1//6*a^-3*(d+3*c*a^2)*log(1+-1*a^2*x^2))
@test integrate((c+d*x^2)^-1*arctanh(a*x), x) == :(-1//4*d^-1//2*(-1c)^-1//2*Polylogarithms.polylog(2,-1*d^(1/2)*(-1*d^(1/2)+a*(-1c)^(1/2))^-1*(1+a*x))+-1//4*d^-1//2*(-1c)^-1//2*Polylogarithms.polylog(2,-1*d^(1/2)*(-1*d^(1/2)+a*(-1c)^(1/2))^-1*(1+-1*a*x))+1//4*d^-1//2*(-1c)^-1//2*Polylogarithms.polylog(2,d^(1/2)*(d^(1/2)+a*(-1c)^(1/2))^-1*(1+a*x))+1//4*d^-1//2*(-1c)^-1//2*Polylogarithms.polylog(2,d^(1/2)*(d^(1/2)+a*(-1c)^(1/2))^-1*(1+-1*a*x))+-1//4*d^-1//2*(-1c)^-1//2*log(a*(-1*d^(1/2)+a*(-1c)^(1/2))^-1*((-1c)^(1/2)+x*d^(1/2)))*log(1+a*x)+-1//4*d^-1//2*(-1c)^-1//2*log(a*(-1*d^(1/2)+a*(-1c)^(1/2))^-1*((-1c)^(1/2)+-1*x*d^(1/2)))*log(1+-1*a*x)+1//4*d^-1//2*(-1c)^-1//2*log(a*(d^(1/2)+a*(-1c)^(1/2))^-1*((-1c)^(1/2)+x*d^(1/2)))*log(1+-1*a*x)+1//4*d^-1//2*(-1c)^-1//2*log(a*(d^(1/2)+a*(-1c)^(1/2))^-1*((-1c)^(1/2)+-1*x*d^(1/2)))*log(1+a*x))
@test integrate((c+d*x^2)^-2*arctanh(a*x), x) == :((1/2)*x*c^-1*(c+d*x^2)^-1*arctanh(a*x)+(1/2)*c^-3//2*d^-1//2*arctan(x*c^-1//2*d^(1/2))*arctanh(a*x)+-1//4*a*c^-1*(d+c*a^2)^-1*log(c+d*x^2)+-1//8*im*c^-3//2*d^-1//2*Polylogarithms.polylog(2,a*(im*d^(1/2)+a*c^(1/2))^-1*(c^(1/2)+im*x*d^(1/2)))+-1//8*im*c^-3//2*d^-1//2*Polylogarithms.polylog(2,a*(im*d^(1/2)+a*c^(1/2))^-1*(c^(1/2)+-1*im*x*d^(1/2)))+1//4*a*c^-1*(d+c*a^2)^-1*log(1+-1*a^2*x^2)+1//8*im*c^-3//2*d^-1//2*Polylogarithms.polylog(2,a*(a*c^(1/2)+-1*im*d^(1/2))^-1*(c^(1/2)+im*x*d^(1/2)))+1//8*im*c^-3//2*d^-1//2*Polylogarithms.polylog(2,a*(a*c^(1/2)+-1*im*d^(1/2))^-1*(c^(1/2)+-1*im*x*d^(1/2)))+-1//8*im*c^-3//2*d^-1//2*log(-1*d^(1/2)*(-1*d^(1/2)+im*a*c^(1/2))^-1*(1+a*x))*log(1+-1*im*x*c^-1//2*d^(1/2))+-1//8*im*c^-3//2*d^-1//2*log(-1*d^(1/2)*(-1*d^(1/2)+im*a*c^(1/2))^-1*(1+-1*a*x))*log(1+im*x*c^-1//2*d^(1/2))+1//8*im*c^-3//2*d^-1//2*log(d^(1/2)*(d^(1/2)+im*a*c^(1/2))^-1*(1+a*x))*log(1+im*x*c^-1//2*d^(1/2))+1//8*im*c^-3//2*d^-1//2*log(d^(1/2)*(d^(1/2)+im*a*c^(1/2))^-1*(1+-1*a*x))*log(1+-1*im*x*c^-1//2*d^(1/2)))
@test integrate((c+d*x^2)^-3*arctanh(a*x), x) == :(-3//32*im*c^-5//2*d^-1//2*Polylogarithms.polylog(2,a*(im*d^(1/2)+a*c^(1/2))^-1*(c^(1/2)+im*x*d^(1/2)))+-3//32*im*c^-5//2*d^-1//2*Polylogarithms.polylog(2,a*(im*d^(1/2)+a*c^(1/2))^-1*(c^(1/2)+-1*im*x*d^(1/2)))+1//4*x*c^-1*(c+d*x^2)^-2*arctanh(a*x)+1//8*a*c^-1*(c+d*x^2)^-1*(d+c*a^2)^-1+3//8*x*c^-2*(c+d*x^2)^-1*arctanh(a*x)+3//8*c^-5//2*d^-1//2*arctan(x*c^-1//2*d^(1/2))*arctanh(a*x)+3//32*im*c^-5//2*d^-1//2*Polylogarithms.polylog(2,a*(a*c^(1/2)+-1*im*d^(1/2))^-1*(c^(1/2)+im*x*d^(1/2)))+3//32*im*c^-5//2*d^-1//2*Polylogarithms.polylog(2,a*(a*c^(1/2)+-1*im*d^(1/2))^-1*(c^(1/2)+-1*im*x*d^(1/2)))+-3//32*im*c^-5//2*d^-1//2*log(-1*d^(1/2)*(-1*d^(1/2)+im*a*c^(1/2))^-1*(1+a*x))*log(1+-1*im*x*c^-1//2*d^(1/2))+-3//32*im*c^-5//2*d^-1//2*log(-1*d^(1/2)*(-1*d^(1/2)+im*a*c^(1/2))^-1*(1+-1*a*x))*log(1+im*x*c^-1//2*d^(1/2))+-1//16*a*c^-2*(d+c*a^2)^-2*(3d+5*c*a^2)*log(c+d*x^2)+1//16*a*c^-2*(d+c*a^2)^-2*(3d+5*c*a^2)*log(1+-1*a^2*x^2)+3//32*im*c^-5//2*d^-1//2*log(d^(1/2)*(d^(1/2)+im*a*c^(1/2))^-1*(1+a*x))*log(1+im*x*c^-1//2*d^(1/2))+3//32*im*c^-5//2*d^-1//2*log(d^(1/2)*(d^(1/2)+im*a*c^(1/2))^-1*(1+-1*a*x))*log(1+-1*im*x*c^-1//2*d^(1/2)))
@test integrate((a+-1*a*x^2)^-1*(b+-2*b*arctanh(x))^-1, x) == :(-1//2*a^-1*b^-1*log(1+-2*arctanh(x)))
@test integrate((1+-1*x^2)^-1*arctanh(b*x), x) == :(-1//4*Polylogarithms.polylog(2,(1+b)^-1*(1+b*x))+-1//4*Polylogarithms.polylog(2,(1+b)^-1*(1+-1*b*x))+1//4*Polylogarithms.polylog(2,(1+-1b)^-1*(1+b*x))+1//4*Polylogarithms.polylog(2,(1+-1b)^-1*(1+-1*b*x))+-1//4*log(b*(1+b)^-1*(1+x))*log(1+-1*b*x)+-1//4*log(b*(1+b)^-1*(1+-1x))*log(1+b*x)+1//4*log(-1*b*(1+-1b)^-1*(1+x))*log(1+b*x)+1//4*log(-1*b*(1+-1b)^-1*(1+-1x))*log(1+-1*b*x))
@test integrate((1+-1*x^2)^-1*arctanh(a+b*x), x) == :(-1//4*Polylogarithms.polylog(2,(1+a+b)^-1*(1+a+b*x))+-1//4*Polylogarithms.polylog(2,(1+b+-1a)^-1*(1+-1a+-1*b*x))+1//4*Polylogarithms.polylog(2,(1+a+-1b)^-1*(1+a+b*x))+1//4*Polylogarithms.polylog(2,(1+-1a+-1b)^-1*(1+-1a+-1*b*x))+-1//4*log(b*(1+a+b)^-1*(1+-1x))*log(1+a+b*x)+-1//4*log(b*(1+b+-1a)^-1*(1+x))*log(1+-1a+-1*b*x)+1//4*log(-1*b*(1+a+-1b)^-1*(1+x))*log(1+a+b*x)+1//4*log(-1*b*(1+-1a+-1b)^-1*(1+-1x))*log(1+-1a+-1*b*x))
@test integrate((a+b*x)^-1*arctanh(x), x) == :((1/2)*b^-1*Polylogarithms.polylog(2,1+-2*(1+x)^-1)+-1//2*b^-1*Polylogarithms.polylog(2,1+-1*(1+x)^-1*(a+b)^-1*(2a+2*b*x))+b^-1*arctanh(x)*log((1+x)^-1*(a+b)^-1*(2a+2*b*x))+-1*b^-1*arctanh(x)*log(2*(1+x)^-1))
@test integrate((a+b*x^2)^-1*arctanh(x), x) == :(-1//4*b^-1//2*(-1a)^-1//2*Polylogarithms.polylog(2,-1*b^(1/2)*((-1a)^(1/2)+-1*b^(1/2))^-1*(1+x))+-1//4*b^-1//2*(-1a)^-1//2*Polylogarithms.polylog(2,-1*b^(1/2)*((-1a)^(1/2)+-1*b^(1/2))^-1*(1+-1x))+1//4*b^-1//2*(-1a)^-1//2*Polylogarithms.polylog(2,b^(1/2)*(b^(1/2)+(-1a)^(1/2))^-1*(1+x))+1//4*b^-1//2*(-1a)^-1//2*Polylogarithms.polylog(2,b^(1/2)*(b^(1/2)+(-1a)^(1/2))^-1*(1+-1x))+-1//4*b^-1//2*(-1a)^-1//2*log(((-1a)^(1/2)+-1*b^(1/2))^-1*((-1a)^(1/2)+x*b^(1/2)))*log(1+x)+-1//4*b^-1//2*(-1a)^-1//2*log(((-1a)^(1/2)+-1*b^(1/2))^-1*((-1a)^(1/2)+-1*x*b^(1/2)))*log(1+-1x)+1//4*b^-1//2*(-1a)^-1//2*log((b^(1/2)+(-1a)^(1/2))^-1*((-1a)^(1/2)+x*b^(1/2)))*log(1+-1x)+1//4*b^-1//2*(-1a)^-1//2*log((b^(1/2)+(-1a)^(1/2))^-1*((-1a)^(1/2)+-1*x*b^(1/2)))*log(1+x))
@test integrate((a+b*x+c*x^2)^-1*arctanh(x), x) == :((1/2)*(b^2+-4*a*c)^-1//2*Polylogarithms.polylog(2,1+-1*(1+x)^-1*(b+(b^2+-4*a*c)^(1/2)+2c)^-1*(2b+2*(b^2+-4*a*c)^(1/2)+4*c*x))+-1//2*(b^2+-4*a*c)^-1//2*Polylogarithms.polylog(2,1+-1*(1+x)^-1*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1*(-2*(b^2+-4*a*c)^(1/2)+2b+4*c*x))+(b^2+-4*a*c)^-1//2*arctanh(x)*log((1+x)^-1*(b+-1*(b^2+-4*a*c)^(1/2)+2c)^-1*(-2*(b^2+-4*a*c)^(1/2)+2b+4*c*x))+-1*(b^2+-4*a*c)^-1//2*arctanh(x)*log((1+x)^-1*(b+(b^2+-4*a*c)^(1/2)+2c)^-1*(2b+2*(b^2+-4*a*c)^(1/2)+4*c*x)))
@test integrate((c+d*x^2)^-3//2*arctanh(a*x), x) == :(-1*c^-1*(d+c*a^2)^-1//2*arctanh(a*(c+d*x^2)^(1/2)*(d+c*a^2)^-1//2)+x*c^-1*(c+d*x^2)^-1//2*arctanh(a*x))
@test integrate((c+d*x^2)^-5//2*arctanh(a*x), x) == :(-1//3*c^-2*(d+c*a^2)^-3//2*(2d+3*c*a^2)*arctanh(a*(c+d*x^2)^(1/2)*(d+c*a^2)^-1//2)+1//3*a*c^-1*(c+d*x^2)^-1//2*(d+c*a^2)^-1+1//3*x*c^-1*(c+d*x^2)^-3//2*arctanh(a*x)+2//3*x*c^-2*(c+d*x^2)^-1//2*arctanh(a*x))
@test integrate((c+d*x^2)^-7//2*arctanh(a*x), x) == :(-1//15*c^-3*(d+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)*(d+c*a^2)^-1//2)+1//5*x*c^-1*(c+d*x^2)^-5//2*arctanh(a*x)+1//15*a*c^-1*(c+d*x^2)^-3//2*(d+c*a^2)^-1+4//15*x*c^-2*(c+d*x^2)^-3//2*arctanh(a*x)+8//15*x*c^-3*(c+d*x^2)^-1//2*arctanh(a*x)+1//15*a*c^-2*(c+d*x^2)^-1//2*(d+c*a^2)^-2*(4d+7*c*a^2))
@test integrate((c+d*x^2)^-9//2*arctanh(a*x), x) == :(-1//35*c^-4*(d+c*a^2)^-7//2*(16*d^3+35*a^6*c^3+56*c*a^2*d^2+70*d*a^4*c^2)*arctanh(a*(c+d*x^2)^(1/2)*(d+c*a^2)^-1//2)+1//7*x*c^-1*(c+d*x^2)^-7//2*arctanh(a*x)+1//35*a*c^-1*(c+d*x^2)^-5//2*(d+c*a^2)^-1+6//35*x*c^-2*(c+d*x^2)^-5//2*arctanh(a*x)+8//35*x*c^-3*(c+d*x^2)^-3//2*arctanh(a*x)+16//35*x*c^-4*(c+d*x^2)^-1//2*arctanh(a*x)+1//35*a*c^-3*(c+d*x^2)^-1//2*(d+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*(d+c*a^2)^-2*(6d+11*c*a^2))
@test integrate((a+-1*a*x^2)^(1/2)*arctanh(x), x) == :((1/2)*(a+-1*a*x^2)^(1/2)+(1/2)*x*(a+-1*a*x^2)^(1/2)*arctanh(x)+(1/2)*im*a*(1+-1*x^2)^(1/2)*(a+-1*a*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+x)^-1//2*(1+-1x)^(1/2))+-1*a*(1+-1*x^2)^(1/2)*(a+-1*a*x^2)^-1//2*arctan((1+x)^-1//2*(1+-1x)^(1/2))*arctanh(x)+-1//2*im*a*(1+-1*x^2)^(1/2)*(a+-1*a*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+x)^-1//2*(1+-1x)^(1/2)))
@test integrate((a+-1*a*x^2)^-1//2*arctanh(x), x) == :(im*(1+-1*x^2)^(1/2)*(a+-1*a*x^2)^-1//2*Polylogarithms.polylog(2,im*(1+x)^-1//2*(1+-1x)^(1/2))+-1*im*(1+-1*x^2)^(1/2)*(a+-1*a*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*(1+x)^-1//2*(1+-1x)^(1/2))+-2*(1+-1*x^2)^(1/2)*(a+-1*a*x^2)^-1//2*arctan((1+x)^-1//2*(1+-1x)^(1/2))*arctanh(x))
@test integrate((a+-1*a*x^2)^-3//2*arctanh(x), x) == :(-1*a^-1*(a+-1*a*x^2)^-1//2+x*a^-1*(a+-1*a*x^2)^-1//2*arctanh(x))
@test integrate((a+-1*a*x^2)^-5//2*arctanh(x), x) == :(-2//3*a^-2*(a+-1*a*x^2)^-1//2+-1//9*a^-1*(a+-1*a*x^2)^-3//2+1//3*x*a^-1*(a+-1*a*x^2)^-3//2*arctanh(x)+2//3*x*a^-2*(a+-1*a*x^2)^-1//2*arctanh(x))
@test integrate((a+-1*a*x^2)^-7//2*arctanh(x), x) == :(-8//15*a^-3*(a+-1*a*x^2)^-1//2+-4//45*a^-2*(a+-1*a*x^2)^-3//2+-1//25*a^-1*(a+-1*a*x^2)^-5//2+1//5*x*a^-1*(a+-1*a*x^2)^-5//2*arctanh(x)+4//15*x*a^-2*(a+-1*a*x^2)^-3//2*arctanh(x)+8//15*x*a^-3*(a+-1*a*x^2)^-1//2*arctanh(x))
@test integrate(x^4*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(-2//25*a*e*x^5+1//5*x^5*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2))+-77//300*b*e*c^-3*x^2+-23//75*b*e*c^-5*log(1+-1*c^2*x^2)+-9//200*b*e*c^-1*x^4+-2//5*a*e*x*c^-4+-2//15*a*e*c^-2*x^3+-2//25*b*e*x^5*arctanh(c*x)+-1//20*b*e*c^-5*log(1+-1*c^2*x^2)^2+-1//20*e*c^-5*(3b+4a)*log(1+-1*c*x)+1//5*b*e*c^-5*arctanh(c*x)^2+1//10*b*c^-5*(d+e*log(1+-1*c^2*x^2))*log(1+-1*c^2*x^2)+1//10*b*c^-3*x^2*(d+e*log(1+-1*c^2*x^2))+1//20*b*c^-1*x^4*(d+e*log(1+-1*c^2*x^2))+1//20*e*c^-5*(-3b+4a)*log(1+c*x)+-2//5*b*e*x*c^-4*arctanh(c*x)+-2//15*b*e*c^-2*x^3*arctanh(c*x))
@test integrate(x^3*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(-1//8*e*x^4*(a+b*arctanh(c*x))+1//4*x^4*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2))+-2//3*b*e*x*c^-3+-1//4*e*c^-4*(a+b*arctanh(c*x))*log(1+-1*c^2*x^2)+-1//4*e*c^-2*x^2*(a+b*arctanh(c*x))+-1//8*b*c^-4*(-3*e+2d)*arctanh(c*x)+-1//18*b*e*c^-1*x^3+1//8*b*x*c^-3*(-3*e+2d)+1//24*b*c^-1*x^3*(-1*e+2d)+2//3*b*e*c^-4*arctanh(c*x)+1//4*b*e*x*c^-3*log(1+-1*c^2*x^2)+1//12*b*e*c^-1*x^3*log(1+-1*c^2*x^2))
@test integrate(x^2*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(-2//9*a*e*x^3+1//3*x^3*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2))+-5//18*b*e*c^-1*x^2+-4//9*b*e*c^-3*log(1+-1*c^2*x^2)+-2//3*a*e*x*c^-2+-2//9*b*e*x^3*arctanh(c*x)+-1//6*e*c^-3*(b+2a)*log(1+-1*c*x)+-1//12*b*e*c^-3*log(1+-1*c^2*x^2)^2+1//3*b*e*c^-3*arctanh(c*x)^2+1//6*b*c^-1*x^2*(d+e*log(1+-1*c^2*x^2))+1//6*b*c^-3*(d+e*log(1+-1*c^2*x^2))*log(1+-1*c^2*x^2)+1//6*e*c^-3*(-1b+2a)*log(1+c*x)+-2//3*b*e*x*c^-2*arctanh(c*x))
@test integrate(x*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :((1/2)*d*x^2*(a+b*arctanh(c*x))+-1//2*e*x^2*(a+b*arctanh(c*x))+b*e*c^-2*arctanh(c*x)+(1/2)*b*x*c^-1*(d+-1*e)+-1*b*e*x*c^-1+-1//2*b*c^-2*(d+-1*e)*arctanh(c*x)+(1/2)*b*e*x*c^-1*log(1+-1*c^2*x^2)+-1//2*e*c^-2*(1+-1*c^2*x^2)*(a+b*arctanh(c*x))*log(1+-1*c^2*x^2))
@test integrate((a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(x*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2))+-2*a*e*x+e*b^-1*c^-1*(a+b*arctanh(c*x))^2+-1*b*e*c^-1*log(1+-1*c^2*x^2)+-2*b*e*x*arctanh(c*x)+1//4*b*c^-1*e^-1*(d+e*log(1+-1*c^2*x^2))^2)
@test integrate(x^-1*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(a*d*log(x)+b*e*Polylogarithms.polylog(3,1+-1*c*x)+(1/2)*b*d*Polylogarithms.polylog(2,c*x)+-1*b*e*Polylogarithms.polylog(3,1+c*x)+-1//2*a*e*Polylogarithms.polylog(2,c^2*x^2)+-1//2*b*d*Polylogarithms.polylog(2,-1*c*x)+b*e*Polylogarithms.polylog(2,1+c*x)*log(1+c*x)+(1/2)*b*e*log(1+c*x)^2*log(-1*c*x)+(1/2)*b*e*(-1*log(1+-1*c^2*x^2)+log(1+c*x)+log(1+-1*c*x))*Polylogarithms.polylog(2,-1*c*x)+-1*b*e*Polylogarithms.polylog(2,1+-1*c*x)*log(1+-1*c*x)+-1//2*b*e*log(1+-1*c*x)^2*log(c*x)+-1//2*b*e*(-1*log(1+-1*c^2*x^2)+log(1+c*x)+log(1+-1*c*x))*Polylogarithms.polylog(2,c*x))
@test integrate(x^-2*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(-1*x^-1*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2))+(1/2)*b*c*(d+e*log(1+-1*c^2*x^2))*log(1+-1*(1+-1*c^2*x^2)^-1)+-1*c*e*b^-1*(a+b*arctanh(c*x))^2+-1//2*b*c*e*Polylogarithms.polylog(2,(1+-1*c^2*x^2)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(-1//2*x^-2*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2))+e*c^2*((1/2)*a+(1/2)*b)*log(1+-1*c*x)+e*c^2*((1/2)*a+-1//2*b)*log(1+c*x)+(1/2)*b*e*c^2*Polylogarithms.polylog(2,-1*c*x)+(1/2)*b*c^2*(d+e*log(1+-1*c^2*x^2))*arctanh(c*x)+-1*a*e*c^2*log(x)+-1//2*b*c*x^-1*(d+e*log(1+-1*c^2*x^2))+-1//2*b*e*c^2*Polylogarithms.polylog(2,c*x))
@test integrate(x^-4*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(-1//3*x^-3*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2))+-1*b*e*c^3*log(x)+-1//3*e*b^-1*c^3*(a+b*arctanh(c*x))^2+-1//6*b*e*c^3*Polylogarithms.polylog(2,(1+-1*c^2*x^2)^-1)+1//3*b*e*c^3*log(1+-1*c^2*x^2)+1//6*b*c^3*(d+e*log(1+-1*c^2*x^2))*log(1+-1*(1+-1*c^2*x^2)^-1)+2//3*e*c^2*x^-1*(a+b*arctanh(c*x))+-1//6*b*c*x^-2*(1+-1*c^2*x^2)*(d+e*log(1+-1*c^2*x^2)))
@test integrate(x^-5*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(-1//4*x^-4*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2))+e*c^4*(-1//3*b+1//4*a)*log(1+c*x)+e*c^4*(1//3*b+1//4*a)*log(1+-1*c*x)+-1//2*a*e*c^4*log(x)+-1//4*b*e*c^4*Polylogarithms.polylog(2,c*x)+-1//4*b*e*c^4*arctanh(c*x)+-1//4*b*c^3*x^-1*(d+e*log(1+-1*c^2*x^2))+-1//12*b*c*x^-3*(d+e*log(1+-1*c^2*x^2))+1//4*a*e*c^2*x^-2+1//4*b*e*c^4*Polylogarithms.polylog(2,-1*c*x)+1//4*b*c^4*(d+e*log(1+-1*c^2*x^2))*arctanh(c*x)+5//12*b*e*c^3*x^-1+1//4*b*e*c^2*x^-2*arctanh(c*x))
@test integrate(x^-6*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2)), x) == :(-1//5*x^-5*(a+b*arctanh(c*x))*(d+e*log(1+-1*c^2*x^2))+-5//6*b*e*c^5*log(x)+-1//5*e*b^-1*c^5*(a+b*arctanh(c*x))^2+-1//10*b*e*c^5*Polylogarithms.polylog(2,(1+-1*c^2*x^2)^-1)+-1//20*b*c*x^-4*(d+e*log(1+-1*c^2*x^2))+1//10*b*c^5*(d+e*log(1+-1*c^2*x^2))*log(1+-1*(1+-1*c^2*x^2)^-1)+2//5*e*c^4*x^-1*(a+b*arctanh(c*x))+2//15*e*c^2*x^-3*(a+b*arctanh(c*x))+7//60*b*e*c^3*x^-2+19//60*b*e*c^5*log(1+-1*c^2*x^2)+-1//10*b*c^3*x^-2*(1+-1*c^2*x^2)*(d+e*log(1+-1*c^2*x^2)))
@test integrate(x*(a+b*arctanh(c*x))*(d+e*log(f+g*x^2)), x) == :((1/2)*d*x^2*(a+b*arctanh(c*x))+-1//2*e*x^2*(a+b*arctanh(c*x))+(1/2)*b*x*c^-1*(d+-1*e)+-1*b*e*x*c^-1+-1//2*b*c^-2*(d+-1*e)*arctanh(c*x)+(1/2)*b*e*x*c^-1*log(f+g*x^2)+(1/2)*e*g^-1*(a+b*arctanh(c*x))*(f+g*x^2)*log(f+g*x^2)+b*e*c^-1*f^(1/2)*g^-1//2*arctan(x*f^-1//2*g^(1/2))+(1/2)*b*e*c^-2*g^-1*(g+f*c^2)*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+-1//4*b*e*c^-2*g^-1*(g+f*c^2)*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))+-1//4*b*e*c^-2*g^-1*(g+f*c^2)*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))+(1/2)*b*e*c^-2*g^-1*(g+f*c^2)*arctanh(c*x)*log(2*c*(1+c*x)^-1*(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*(g+f*c^2)*arctanh(c*x)*log(2*c*(1+c*x)^-1*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))+-1*b*e*c^-2*g^-1*(g+f*c^2)*arctanh(c*x)*log(2*(1+c*x)^-1)+-1//2*b*e*c^-2*g^-1*(g+f*c^2)*arctanh(c*x)*log(f+g*x^2))
@test integrate((a+b*arctanh(c*x))*(d+e*log(f+g*x^2)), x) == :(x*(a+b*arctanh(c*x))*(d+e*log(f+g*x^2))+-2*a*e*x+(1/2)*b*e*c^-1*Polylogarithms.polylog(2,c^2*(g+f*c^2)^-1*(f+g*x^2))+(1/2)*b*c^-1*(d+e*log(f+g*x^2))*log(g*(g+f*c^2)^-1*(1+-1*c^2*x^2))+-1*b*e*c^-1*log(1+-1*c^2*x^2)+-2*b*e*x*arctanh(c*x)+(1/2)*b*e*g^-1//2*(-1*f)^(1/2)*Polylogarithms.polylog(2,-1*g^(1/2)*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*(1+c*x))+(1/2)*b*e*g^-1//2*(-1*f)^(1/2)*Polylogarithms.polylog(2,-1*g^(1/2)*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*(1+-1*c*x))+2*a*e*f^(1/2)*g^-1//2*arctan(x*f^-1//2*g^(1/2))+-1//2*b*e*g^-1//2*(-1*f)^(1/2)*Polylogarithms.polylog(2,g^(1/2)*(g^(1/2)+c*(-1*f)^(1/2))^-1*(1+c*x))+-1//2*b*e*g^-1//2*(-1*f)^(1/2)*Polylogarithms.polylog(2,g^(1/2)*(g^(1/2)+c*(-1*f)^(1/2))^-1*(1+-1*c*x))+(1/2)*b*e*g^-1//2*(-1*f)^(1/2)*log(c*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))*log(1+c*x)+(1/2)*b*e*g^-1//2*(-1*f)^(1/2)*log(c*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))*log(1+-1*c*x)+-1//2*b*e*g^-1//2*(-1*f)^(1/2)*log(c*(g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))*log(1+-1*c*x)+-1//2*b*e*g^-1//2*(-1*f)^(1/2)*log(c*(g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))*log(1+c*x))
@test integrate(x^-2*(a+b*arctanh(c*x))*(d+e*log(f+g*x^2)), x) == :(-1*x^-1*(a+b*arctanh(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*(g+f*c^2)^-1*(f+g*x^2))+-1//2*b*c*(d+e*log(f+g*x^2))*log(g*(g+f*c^2)^-1*(1+-1*c^2*x^2))+(1/2)*b*e*g^(1/2)*(-1*f)^-1//2*Polylogarithms.polylog(2,g^(1/2)*(g^(1/2)+c*(-1*f)^(1/2))^-1*(1+c*x))+(1/2)*b*e*g^(1/2)*(-1*f)^-1//2*Polylogarithms.polylog(2,g^(1/2)*(g^(1/2)+c*(-1*f)^(1/2))^-1*(1+-1*c*x))+2*a*e*f^-1//2*g^(1/2)*arctan(x*f^-1//2*g^(1/2))+-1//2*b*e*g^(1/2)*(-1*f)^-1//2*Polylogarithms.polylog(2,-1*g^(1/2)*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*(1+c*x))+-1//2*b*e*g^(1/2)*(-1*f)^-1//2*Polylogarithms.polylog(2,-1*g^(1/2)*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*(1+-1*c*x))+(1/2)*b*e*g^(1/2)*(-1*f)^-1//2*log(c*(g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))*log(1+-1*c*x)+(1/2)*b*e*g^(1/2)*(-1*f)^-1//2*log(c*(g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))*log(1+c*x)+-1//2*b*e*g^(1/2)*(-1*f)^-1//2*log(c*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))*log(1+c*x)+-1//2*b*e*g^(1/2)*(-1*f)^-1//2*log(c*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))*log(1+-1*c*x))
@test integrate(x^-3*(a+b*arctanh(c*x))*(d+e*log(f+g*x^2)), x) == :(-1//2*x^-2*(a+b*arctanh(c*x))*(d+e*log(f+g*x^2))+(1/2)*b*c^2*(d+e*log(f+g*x^2))*arctanh(c*x)+-1//2*b*c*x^-1*(d+e*log(f+g*x^2))+a*e*g*f^-1*log(x)+(1/2)*b*e*g*f^-1*Polylogarithms.polylog(2,c*x)+-1//2*a*e*g*f^-1*log(f+g*x^2)+-1//2*b*e*g*f^-1*Polylogarithms.polylog(2,-1*c*x)+-1//2*b*e*f^-1*(g+f*c^2)*Polylogarithms.polylog(2,1+-2*(1+c*x)^-1)+1//4*b*e*f^-1*(g+f*c^2)*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))+1//4*b*e*f^-1*(g+f*c^2)*Polylogarithms.polylog(2,1+-2*c*(1+c*x)^-1*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2)))+b*c*e*f^-1//2*g^(1/2)*arctan(x*f^-1//2*g^(1/2))+b*e*f^-1*(g+f*c^2)*arctanh(c*x)*log(2*(1+c*x)^-1)+-1//2*b*e*f^-1*(g+f*c^2)*arctanh(c*x)*log(2*c*(1+c*x)^-1*(g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+x*g^(1/2)))+-1//2*b*e*f^-1*(g+f*c^2)*arctanh(c*x)*log(2*c*(1+c*x)^-1*(-1*g^(1/2)+c*(-1*f)^(1/2))^-1*((-1*f)^(1/2)+-1*x*g^(1/2))))

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.4 u (a+b arctanh(c x))^p.jl