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

@test integrate(x^5*(a+b*arctanh(c*x)), x) == :(1//6*x^6*(a+b*arctanh(c*x))+-1//6*b*c^-6*arctanh(c*x)+1//6*b*x*c^-5+1//18*b*c^-3*x^3+1//30*b*c^-1*x^5)
@test integrate(x^4*(a+b*arctanh(c*x)), x) == :(1//5*x^5*(a+b*arctanh(c*x))+1//10*b*c^-5*log(1+-1*c^2*x^2)+1//10*b*c^-3*x^2+1//20*b*c^-1*x^4)
@test integrate(x^3*(a+b*arctanh(c*x)), x) == :(1//4*x^4*(a+b*arctanh(c*x))+-1//4*b*c^-4*arctanh(c*x)+1//4*b*x*c^-3+1//12*b*c^-1*x^3)
@test integrate(x^2*(a+b*arctanh(c*x)), x) == :(1//3*x^3*(a+b*arctanh(c*x))+1//6*b*c^-1*x^2+1//6*b*c^-3*log(1+-1*c^2*x^2))
@test integrate(x*(a+b*arctanh(c*x)), x) == :((1/2)*x^2*(a+b*arctanh(c*x))+(1/2)*b*x*c^-1+-1//2*b*c^-2*arctanh(c*x))
@test integrate(a+b*arctanh(c*x), x) == :(a*x+b*x*arctanh(c*x)+(1/2)*b*c^-1*log(1+-1*c^2*x^2))
@test integrate(x^-1*(a+b*arctanh(c*x)), x) == :(a*log(x)+(1/2)*b*Polylogarithms.polylog(2,c*x)+-1//2*b*Polylogarithms.polylog(2,-1*c*x))
@test integrate(x^-2*(a+b*arctanh(c*x)), x) == :(-1*x^-1*(a+b*arctanh(c*x))+b*c*log(x)+-1//2*b*c*log(1+-1*c^2*x^2))
@test integrate(x^-3*(a+b*arctanh(c*x)), x) == :(-1//2*x^-2*(a+b*arctanh(c*x))+(1/2)*b*c^2*arctanh(c*x)+-1//2*b*c*x^-1)
@test integrate(x^-4*(a+b*arctanh(c*x)), x) == :(-1//3*x^-3*(a+b*arctanh(c*x))+-1//6*b*c*x^-2+-1//6*b*c^3*log(1+-1*c^2*x^2)+1//3*b*c^3*log(x))
@test integrate(x^-5*(a+b*arctanh(c*x)), x) == :(-1//4*x^-4*(a+b*arctanh(c*x))+-1//4*b*c^3*x^-1+-1//12*b*c*x^-3+1//4*b*c^4*arctanh(c*x))
@test integrate(x^-6*(a+b*arctanh(c*x)), x) == :(-1//5*x^-5*(a+b*arctanh(c*x))+-1//10*b*c^3*x^-2+-1//10*b*c^5*log(1+-1*c^2*x^2)+-1//20*b*c*x^-4+1//5*b*c^5*log(x))
@test integrate(x^5*(a+b*arctanh(c*x))^2, x) == :(-1//6*c^-6*(a+b*arctanh(c*x))^2+1//6*x^6*(a+b*arctanh(c*x))^2+1//60*b^2*c^-2*x^4+4//45*b^2*c^-4*x^2+23//90*b^2*c^-6*log(1+-1*c^2*x^2)+1//3*a*b*x*c^-5+1//3*x*b^2*c^-5*arctanh(c*x)+1//9*b*c^-3*x^3*(a+b*arctanh(c*x))+1//15*b*c^-1*x^5*(a+b*arctanh(c*x)))
@test integrate(x^4*(a+b*arctanh(c*x))^2, x) == :(1//5*c^-5*(a+b*arctanh(c*x))^2+1//5*x^5*(a+b*arctanh(c*x))^2+-3//10*b^2*c^-5*arctanh(c*x)+-1//5*b^2*c^-5*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//30*b^2*c^-2*x^3+3//10*x*b^2*c^-4+-2//5*b*c^-5*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//5*b*c^-3*x^2*(a+b*arctanh(c*x))+1//10*b*c^-1*x^4*(a+b*arctanh(c*x)))
@test integrate(x^3*(a+b*arctanh(c*x))^2, x) == :(-1//4*c^-4*(a+b*arctanh(c*x))^2+1//4*x^4*(a+b*arctanh(c*x))^2+1//3*b^2*c^-4*log(1+-1*c^2*x^2)+1//12*b^2*c^-2*x^2+(1/2)*a*b*x*c^-3+(1/2)*x*b^2*c^-3*arctanh(c*x)+1//6*b*c^-1*x^3*(a+b*arctanh(c*x)))
@test integrate(x^2*(a+b*arctanh(c*x))^2, x) == :(1//3*c^-3*(a+b*arctanh(c*x))^2+1//3*x^3*(a+b*arctanh(c*x))^2+-1//3*b^2*c^-3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//3*b^2*c^-3*arctanh(c*x)+1//3*x*b^2*c^-2+-2//3*b*c^-3*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//3*b*c^-1*x^2*(a+b*arctanh(c*x)))
@test integrate(x*(a+b*arctanh(c*x))^2, x) == :((1/2)*x^2*(a+b*arctanh(c*x))^2+-1//2*c^-2*(a+b*arctanh(c*x))^2+(1/2)*b^2*c^-2*log(1+-1*c^2*x^2)+a*b*x*c^-1+x*b^2*c^-1*arctanh(c*x))
@test integrate((a+b*arctanh(c*x))^2, x) == :(x*(a+b*arctanh(c*x))^2+c^-1*(a+b*arctanh(c*x))^2+-1*b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-2*b*c^-1*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x))^2, x) == :((1/2)*b^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+2*(a+b*arctanh(c*x))^2*arctanh(1+-2*(1+-1*c*x)^-1)+-1//2*b^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+b*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+-1*b*(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, x) == :(c*(a+b*arctanh(c*x))^2+-1*x^-1*(a+b*arctanh(c*x))^2+-1*c*b^2*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+2*b*c*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x))^2, x) == :((1/2)*c^2*(a+b*arctanh(c*x))^2+-1//2*x^-2*(a+b*arctanh(c*x))^2+b^2*c^2*log(x)+-1//2*b^2*c^2*log(1+-1*c^2*x^2)+-1*b*c*x^-1*(a+b*arctanh(c*x)))
@test integrate(x^-4*(a+b*arctanh(c*x))^2, x) == :(-1//3*x^-3*(a+b*arctanh(c*x))^2+1//3*c^3*(a+b*arctanh(c*x))^2+-1//3*b^2*c^2*x^-1+-1//3*b^2*c^3*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+1//3*b^2*c^3*arctanh(c*x)+-1//3*b*c*x^-2*(a+b*arctanh(c*x))+2//3*b*c^3*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1))
@test integrate(x^-5*(a+b*arctanh(c*x))^2, x) == :(-1//4*x^-4*(a+b*arctanh(c*x))^2+1//4*c^4*(a+b*arctanh(c*x))^2+-1//3*b^2*c^4*log(1+-1*c^2*x^2)+-1//12*b^2*c^2*x^-2+2//3*b^2*c^4*log(x)+-1//2*b*c^3*x^-1*(a+b*arctanh(c*x))+-1//6*b*c*x^-3*(a+b*arctanh(c*x)))
@test integrate(x^5*(a+b*arctanh(c*x))^3, x) == :(-1//6*c^-6*(a+b*arctanh(c*x))^3+1//6*x^6*(a+b*arctanh(c*x))^3+-23//30*b^3*c^-6*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-19//60*b^3*c^-6*arctanh(c*x)+1//60*b^3*c^-3*x^3+19//60*x*b^3*c^-5+23//30*b*c^-6*(a+b*arctanh(c*x))^2+(1/2)*b*x*c^-5*(a+b*arctanh(c*x))^2+-23//15*b^2*c^-6*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//6*b*c^-3*x^3*(a+b*arctanh(c*x))^2+1//10*b*c^-1*x^5*(a+b*arctanh(c*x))^2+1//20*b^2*c^-2*x^4*(a+b*arctanh(c*x))+4//15*b^2*c^-4*x^2*(a+b*arctanh(c*x)))
@test integrate(x^4*(a+b*arctanh(c*x))^3, x) == :(1//5*c^-5*(a+b*arctanh(c*x))^3+1//5*x^5*(a+b*arctanh(c*x))^3+(1/2)*b^3*c^-5*log(1+-1*c^2*x^2)+-9//20*b*c^-5*(a+b*arctanh(c*x))^2+1//20*b^3*c^-3*x^2+3//10*b^3*c^-5*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+-3//5*b*c^-5*(a+b*arctanh(c*x))^2*log(2*(1+-1*c*x)^-1)+-3//5*b^2*c^-5*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+1//10*b^2*c^-2*x^3*(a+b*arctanh(c*x))+3//10*b*c^-3*x^2*(a+b*arctanh(c*x))^2+3//20*b*c^-1*x^4*(a+b*arctanh(c*x))^2+9//10*a*x*b^2*c^-4+9//10*x*b^3*c^-4*arctanh(c*x))
@test integrate(x^3*(a+b*arctanh(c*x))^3, x) == :(-1//4*c^-4*(a+b*arctanh(c*x))^3+1//4*x^4*(a+b*arctanh(c*x))^3+b*c^-4*(a+b*arctanh(c*x))^2+-1*b^3*c^-4*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-1//4*b^3*c^-4*arctanh(c*x)+1//4*x*b^3*c^-3+-2*b^2*c^-4*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+1//4*b*c^-1*x^3*(a+b*arctanh(c*x))^2+1//4*b^2*c^-2*x^2*(a+b*arctanh(c*x))+3//4*b*x*c^-3*(a+b*arctanh(c*x))^2)
@test integrate(x^2*(a+b*arctanh(c*x))^3, x) == :(1//3*c^-3*(a+b*arctanh(c*x))^3+1//3*x^3*(a+b*arctanh(c*x))^3+(1/2)*b^3*c^-3*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1)+(1/2)*b^3*c^-3*log(1+-1*c^2*x^2)+-1//2*b*c^-3*(a+b*arctanh(c*x))^2+a*x*b^2*c^-2+x*b^3*c^-2*arctanh(c*x)+(1/2)*b*c^-1*x^2*(a+b*arctanh(c*x))^2+-1*b*c^-3*(a+b*arctanh(c*x))^2*log(2*(1+-1*c*x)^-1)+-1*b^2*c^-3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1))
@test integrate(x*(a+b*arctanh(c*x))^3, x) == :((1/2)*x^2*(a+b*arctanh(c*x))^3+-1//2*c^-2*(a+b*arctanh(c*x))^3+-3//2*b^3*c^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+3//2*b*c^-2*(a+b*arctanh(c*x))^2+-3*b^2*c^-2*(a+b*arctanh(c*x))*log(2*(1+-1*c*x)^-1)+3//2*b*x*c^-1*(a+b*arctanh(c*x))^2)
@test integrate((a+b*arctanh(c*x))^3, x) == :(x*(a+b*arctanh(c*x))^3+c^-1*(a+b*arctanh(c*x))^3+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))
@test integrate(x^-1*(a+b*arctanh(c*x))^3, x) == :(2*(a+b*arctanh(c*x))^3*arctanh(1+-2*(1+-1*c*x)^-1)+-3//4*b^3*Polylogarithms.polylog(4,1+-2*(1+-1*c*x)^-1)+3//4*b^3*Polylogarithms.polylog(4,-1+2*(1+-1*c*x)^-1)+-3//2*b*(a+b*arctanh(c*x))^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x)^-1)+-3//2*b^2*(a+b*arctanh(c*x))*Polylogarithms.polylog(3,-1+2*(1+-1*c*x)^-1)+3//2*b*(a+b*arctanh(c*x))^2*Polylogarithms.polylog(2,-1+2*(1+-1*c*x)^-1)+3//2*b^2*(a+b*arctanh(c*x))*Polylogarithms.polylog(3,1+-2*(1+-1*c*x)^-1))
@test integrate(x^-2*(a+b*arctanh(c*x))^3, x) == :(c*(a+b*arctanh(c*x))^3+-1*x^-1*(a+b*arctanh(c*x))^3+-3//2*c*b^3*Polylogarithms.polylog(3,-1+2*(1+c*x)^-1)+-3*c*b^2*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+3*b*c*(a+b*arctanh(c*x))^2*log(2+-2*(1+c*x)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x))^3, x) == :((1/2)*c^2*(a+b*arctanh(c*x))^3+-1//2*x^-2*(a+b*arctanh(c*x))^3+-3//2*b^3*c^2*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+3//2*b*c^2*(a+b*arctanh(c*x))^2+3*b^2*c^2*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1)+-3//2*b*c*x^-1*(a+b*arctanh(c*x))^2)
@test integrate(x^-4*(a+b*arctanh(c*x))^3, x) == :(-1//3*x^-3*(a+b*arctanh(c*x))^3+1//3*c^3*(a+b*arctanh(c*x))^3+b^3*c^3*log(x)+(1/2)*b*c^3*(a+b*arctanh(c*x))^2+-1//2*b^3*c^3*Polylogarithms.polylog(3,-1+2*(1+c*x)^-1)+-1//2*b^3*c^3*log(1+-1*c^2*x^2)+b*c^3*(a+b*arctanh(c*x))^2*log(2+-2*(1+c*x)^-1)+-1*b^2*c^2*x^-1*(a+b*arctanh(c*x))+-1*b^2*c^3*(a+b*arctanh(c*x))*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1//2*b*c*x^-2*(a+b*arctanh(c*x))^2)
@test integrate(x^-5*(a+b*arctanh(c*x))^3, x) == :(-1//4*x^-4*(a+b*arctanh(c*x))^3+1//4*c^4*(a+b*arctanh(c*x))^3+b*c^4*(a+b*arctanh(c*x))^2+-1*b^3*c^4*Polylogarithms.polylog(2,-1+2*(1+c*x)^-1)+-1//4*b^3*c^3*x^-1+1//4*b^3*c^4*arctanh(c*x)+2*b^2*c^4*(a+b*arctanh(c*x))*log(2+-2*(1+c*x)^-1)+-3//4*b*c^3*x^-1*(a+b*arctanh(c*x))^2+-1//4*b*c*x^-3*(a+b*arctanh(c*x))^2+-1//4*b^2*c^2*x^-2*(a+b*arctanh(c*x)))
@test integrate((d*x)^5//2*(a+b*arctanh(c*x)), x) == :(2//7*d^-1*(d*x)^7//2*(a+b*arctanh(c*x))+4//35*b*c^-1*(d*x)^5//2+-2//7*b*c^-7//2*d^5//2*arctan(c^(1/2)*d^-1//2*(d*x)^(1/2))+-2//7*b*c^-7//2*d^5//2*arctanh(c^(1/2)*d^-1//2*(d*x)^(1/2))+4//7*b*c^-3*d^2*(d*x)^(1/2))
@test integrate((d*x)^3//2*(a+b*arctanh(c*x)), x) == :(2//5*d^-1*(d*x)^5//2*(a+b*arctanh(c*x))+4//15*b*c^-1*(d*x)^3//2+-2//5*b*c^-5//2*d^3//2*arctanh(c^(1/2)*d^-1//2*(d*x)^(1/2))+2//5*b*c^-5//2*d^3//2*arctan(c^(1/2)*d^-1//2*(d*x)^(1/2)))
@test integrate((d*x)^(1/2)*(a+b*arctanh(c*x)), x) == :(2//3*d^-1*(d*x)^3//2*(a+b*arctanh(c*x))+4//3*b*c^-1*(d*x)^(1/2)+-2//3*b*c^-3//2*d^(1/2)*arctan(c^(1/2)*d^-1//2*(d*x)^(1/2))+-2//3*b*c^-3//2*d^(1/2)*arctanh(c^(1/2)*d^-1//2*(d*x)^(1/2)))
@test integrate((d*x)^-1//2*(a+b*arctanh(c*x)), x) == :(2*d^-1*(d*x)^(1/2)*(a+b*arctanh(c*x))+-2*b*c^-1//2*d^-1//2*arctanh(c^(1/2)*d^-1//2*(d*x)^(1/2))+2*b*c^-1//2*d^-1//2*arctan(c^(1/2)*d^-1//2*(d*x)^(1/2)))
@test integrate((d*x)^-3//2*(a+b*arctanh(c*x)), x) == :(-1*d^-1*(d*x)^-1//2*(2a+2*b*arctanh(c*x))+2*b*c^(1/2)*d^-3//2*arctan(c^(1/2)*d^-1//2*(d*x)^(1/2))+2*b*c^(1/2)*d^-3//2*arctanh(c^(1/2)*d^-1//2*(d*x)^(1/2)))
@test integrate((d*x)^-5//2*(a+b*arctanh(c*x)), x) == :(-1//3*d^-1*(d*x)^-3//2*(2a+2*b*arctanh(c*x))+-4//3*b*c*d^-2*(d*x)^-1//2+-2//3*b*c^3//2*d^-5//2*arctan(c^(1/2)*d^-1//2*(d*x)^(1/2))+2//3*b*c^3//2*d^-5//2*arctanh(c^(1/2)*d^-1//2*(d*x)^(1/2)))
@test integrate((d*x)^-7//2*(a+b*arctanh(c*x)), x) == :(-1//5*d^-1*(d*x)^-5//2*(2a+2*b*arctanh(c*x))+-4//15*b*c*d^-2*(d*x)^-3//2+2//5*b*c^5//2*d^-7//2*arctan(c^(1/2)*d^-1//2*(d*x)^(1/2))+2//5*b*c^5//2*d^-7//2*arctanh(c^(1/2)*d^-1//2*(d*x)^(1/2)))
@test integrate((d*x)^-9//2*(a+b*arctanh(c*x)), x) == :(-1//7*d^-1*(d*x)^-7//2*(2a+2*b*arctanh(c*x))+-4//7*b*c^3*d^-4*(d*x)^-1//2+-4//35*b*c*d^-2*(d*x)^-5//2+-2//7*b*c^7//2*d^-9//2*arctan(c^(1/2)*d^-1//2*(d*x)^(1/2))+2//7*b*c^7//2*d^-9//2*arctanh(c^(1/2)*d^-1//2*(d*x)^(1/2)))
@test integrate(x^7*(a+b*arctanh(c*x^2)), x) == :(1//8*x^8*(a+b*arctanh(c*x^2))+-1//8*b*c^-4*arctanh(c*x^2)+1//8*b*c^-3*x^2+1//24*b*c^-1*x^6)
@test integrate(x^5*(a+b*arctanh(c*x^2)), x) == :(1//6*x^6*(a+b*arctanh(c*x^2))+1//12*b*c^-1*x^4+1//12*b*c^-3*log(1+-1*c^2*x^4))
@test integrate(x^3*(a+b*arctanh(c*x^2)), x) == :(1//4*x^4*(a+b*arctanh(c*x^2))+-1//4*b*c^-2*arctanh(c*x^2)+1//4*b*c^-1*x^2)
@test integrate(x*(a+b*arctanh(c*x^2)), x) == :((1/2)*x^2*(a+b*arctanh(c*x^2))+1//4*b*c^-1*log(1+-1*c^2*x^4))
@test integrate(x^-1*(a+b*arctanh(c*x^2)), x) == :(a*log(x)+-1//4*b*Polylogarithms.polylog(2,-1*c*x^2)+1//4*b*Polylogarithms.polylog(2,c*x^2))
@test integrate(x^-3*(a+b*arctanh(c*x^2)), x) == :(-1//2*x^-2*(a+b*arctanh(c*x^2))+b*c*log(x)+-1//4*b*c*log(1+-1*c^2*x^4))
@test integrate(x^-5*(a+b*arctanh(c*x^2)), x) == :(-1//4*x^-4*(a+b*arctanh(c*x^2))+-1//4*b*c*x^-2+1//4*b*c^2*arctanh(c*x^2))
@test integrate(x^-7*(a+b*arctanh(c*x^2)), x) == :(-1//6*x^-6*(a+b*arctanh(c*x^2))+-1//12*b*c*x^-4+-1//12*b*c^3*log(1+-1*c^2*x^4)+1//3*b*c^3*log(x))
@test integrate(x^4*(a+b*arctanh(c*x^2)), x) == :(1//5*x^5*(a+b*arctanh(c*x^2))+-1//5*b*c^-5//2*arctanh(x*c^(1/2))+1//5*b*c^-5//2*arctan(x*c^(1/2))+2//15*b*c^-1*x^3)
@test integrate(x^2*(a+b*arctanh(c*x^2)), x) == :(1//3*x^3*(a+b*arctanh(c*x^2))+-1//3*b*c^-3//2*arctan(x*c^(1/2))+-1//3*b*c^-3//2*arctanh(x*c^(1/2))+2//3*b*x*c^-1)
@test integrate(a+b*arctanh(c*x^2), x) == :(a*x+b*x*arctanh(c*x^2)+b*c^-1//2*arctan(x*c^(1/2))+-1*b*c^-1//2*arctanh(x*c^(1/2)))
@test integrate(x^-2*(a+b*arctanh(c*x^2)), x) == :(-1*x^-1*(a+b*arctanh(c*x^2))+b*c^(1/2)*arctan(x*c^(1/2))+b*c^(1/2)*arctanh(x*c^(1/2)))
@test integrate(x^-4*(a+b*arctanh(c*x^2)), x) == :(-1//3*x^-3*(a+b*arctanh(c*x^2))+-2//3*b*c*x^-1+-1//3*b*c^3//2*arctan(x*c^(1/2))+1//3*b*c^3//2*arctanh(x*c^(1/2)))
@test integrate(x^-6*(a+b*arctanh(c*x^2)), x) == :(-1//5*x^-5*(a+b*arctanh(c*x^2))+-2//15*b*c*x^-3+1//5*b*c^5//2*arctan(x*c^(1/2))+1//5*b*c^5//2*arctanh(x*c^(1/2)))
@test integrate(x^7*(a+b*arctanh(c*x^2))^2, x) == :(-1//8*c^-4*(a+b*arctanh(c*x^2))^2+1//8*x^8*(a+b*arctanh(c*x^2))^2+1//6*b^2*c^-4*log(1+-1*c^2*x^4)+1//24*b^2*c^-2*x^4+1//4*a*b*c^-3*x^2+1//4*b^2*c^-3*x^2*arctanh(c*x^2)+1//12*b*c^-1*x^6*(a+b*arctanh(c*x^2)))
@test integrate(x^5*(a+b*arctanh(c*x^2))^2, x) == :(1//6*c^-3*(a+b*arctanh(c*x^2))^2+1//6*x^6*(a+b*arctanh(c*x^2))^2+-1//6*b^2*c^-3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^2)^-1)+-1//6*b^2*c^-3*arctanh(c*x^2)+1//6*b^2*c^-2*x^2+-1//3*b*c^-3*(a+b*arctanh(c*x^2))*log(2*(1+-1*c*x^2)^-1)+1//6*b*c^-1*x^4*(a+b*arctanh(c*x^2)))
@test integrate(x^3*(a+b*arctanh(c*x^2))^2, x) == :(-1//4*c^-2*(a+b*arctanh(c*x^2))^2+1//4*x^4*(a+b*arctanh(c*x^2))^2+1//4*b^2*c^-2*log(1+-1*c^2*x^4)+(1/2)*a*b*c^-1*x^2+(1/2)*b^2*c^-1*x^2*arctanh(c*x^2))
@test integrate(x*(a+b*arctanh(c*x^2))^2, x) == :((1/2)*c^-1*(a+b*arctanh(c*x^2))^2+(1/2)*x^2*(a+b*arctanh(c*x^2))^2+-1//2*b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^2)^-1)+-1*b*c^-1*(a+b*arctanh(c*x^2))*log(2*(1+-1*c*x^2)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x^2))^2, x) == :((a+b*arctanh(c*x^2))^2*arctanh(1+-2*(1+-1*c*x^2)^-1)+-1//4*b^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^2)^-1)+1//4*b^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^2)^-1)+(1/2)*b*(a+b*arctanh(c*x^2))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^2)^-1)+-1//2*b*(a+b*arctanh(c*x^2))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^2)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x^2))^2, x) == :((1/2)*c*(a+b*arctanh(c*x^2))^2+-1//2*x^-2*(a+b*arctanh(c*x^2))^2+-1//2*c*b^2*Polylogarithms.polylog(2,-1+2*(1+c*x^2)^-1)+b*c*(a+b*arctanh(c*x^2))*log(2+-2*(1+c*x^2)^-1))
@test integrate(x^-5*(a+b*arctanh(c*x^2))^2, x) == :(-1//4*x^-4*(a+b*arctanh(c*x^2))^2+1//4*c^2*(a+b*arctanh(c*x^2))^2+b^2*c^2*log(x)+-1//4*b^2*c^2*log(1+-1*c^2*x^4)+-1//2*b*c*x^-2*(a+b*arctanh(c*x^2)))
@test integrate(x^4*(a+b*arctanh(c*x^2))^2, x) == :(1//20*x^5*(2a+-1*b*log(1+-1*c*x^2))^2+-4//15*b^2*c^-5//2*arctan(x*c^(1/2))+-4//15*b^2*c^-5//2*arctanh(x*c^(1/2))+-2//25*a*b*x^5+-1//5*b^2*c^-5//2*arctanh(x*c^(1/2))^2+-1//10*b^2*c^-5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+-1//10*b^2*c^-5//2*Polylogarithms.polylog(2,1+2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+1//5*b^2*c^-5//2*Polylogarithms.polylog(2,1+-2*(1+x*c^(1/2))^-1)+1//5*b^2*c^-5//2*Polylogarithms.polylog(2,1+-2*(1+-1*x*c^(1/2))^-1)+1//20*b^2*x^5*log(1+c*x^2)^2+1//25*b*x^5*(2a+-1*b*log(1+-1*c*x^2))+1//25*b^2*x^5*log(1+-1*c*x^2)+8//15*x*b^2*c^-2+-2//5*b^2*c^-5//2*arctan(x*c^(1/2))*log(2*(1+-1*im*x*c^(1/2))^-1)+-2//5*b^2*c^-5//2*arctanh(x*c^(1/2))*log(2*(1+x*c^(1/2))^-1)+-1//5*b*c^-5//2*(2a+-1*b*log(1+-1*c*x^2))*arctanh(x*c^(1/2))+-1//5*b^2*c^-5//2*arctan(x*c^(1/2))*log(1+-1*c*x^2)+-1//5*b^2*c^-5//2*arctanh(x*c^(1/2))*log(1+c*x^2)+-1//10*im*b^2*c^-5//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+-1//10*im*b^2*c^-5//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+-1//10*b^2*x^5*log(1+c*x^2)*log(1+-1*c*x^2)+-1//15*b^2*c^-1*x^3*log(1+-1*c*x^2)+1//5*im*b^2*c^-5//2*arctan(x*c^(1/2))^2+1//5*im*b^2*c^-5//2*Polylogarithms.polylog(2,1+-2*(1+im*x*c^(1/2))^-1)+1//5*im*b^2*c^-5//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*x*c^(1/2))^-1)+1//5*a*b*x^5*log(1+c*x^2)+1//5*b^2*c^-5//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+1//5*b^2*c^-5//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+1//5*b^2*c^-5//2*arctan(x*c^(1/2))*log(1+c*x^2)+1//5*b^2*c^-5//2*arctanh(x*c^(1/2))*log(-2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+1//5*b^2*c^-5//2*arctanh(x*c^(1/2))*log(2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+1//15*b*c^-1*x^3*(2a+-1*b*log(1+-1*c*x^2))+2//5*a*b*c^-5//2*arctan(x*c^(1/2))+2//5*b^2*c^-5//2*arctan(x*c^(1/2))*log(2*(1+im*x*c^(1/2))^-1)+2//5*b^2*c^-5//2*arctanh(x*c^(1/2))*log(2*(1+-1*x*c^(1/2))^-1)+2//15*a*b*c^-1*x^3+2//15*b^2*c^-1*x^3*log(1+c*x^2))
@test integrate(x^2*(a+b*arctanh(c*x^2))^2, x) == :(1//12*x^3*(2a+-1*b*log(1+-1*c*x^2))^2+-4//3*b^2*c^-3//2*arctanh(x*c^(1/2))+-2//9*a*b*x^3+-1//3*b^2*c^-3//2*arctanh(x*c^(1/2))^2+-1//6*b^2*c^-3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+-1//6*b^2*c^-3//2*Polylogarithms.polylog(2,1+2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+1//3*b^2*c^-3//2*Polylogarithms.polylog(2,1+-2*(1+x*c^(1/2))^-1)+1//3*b^2*c^-3//2*Polylogarithms.polylog(2,1+-2*(1+-1*x*c^(1/2))^-1)+1//9*b*x^3*(2a+-1*b*log(1+-1*c*x^2))+1//9*b^2*x^3*log(1+-1*c*x^2)+1//12*b^2*x^3*log(1+c*x^2)^2+4//3*b^2*c^-3//2*arctan(x*c^(1/2))+-2//3*a*b*c^-3//2*arctan(x*c^(1/2))+-2//3*x*b^2*c^-1*log(1+-1*c*x^2)+-2//3*b^2*c^-3//2*arctan(x*c^(1/2))*log(2*(1+im*x*c^(1/2))^-1)+-2//3*b^2*c^-3//2*arctanh(x*c^(1/2))*log(2*(1+x*c^(1/2))^-1)+-1//3*im*b^2*c^-3//2*arctan(x*c^(1/2))^2+-1//3*im*b^2*c^-3//2*Polylogarithms.polylog(2,1+-2*(1+im*x*c^(1/2))^-1)+-1//3*im*b^2*c^-3//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*x*c^(1/2))^-1)+-1//3*b*c^-3//2*(2a+-1*b*log(1+-1*c*x^2))*arctanh(x*c^(1/2))+-1//3*b^2*c^-3//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+-1//3*b^2*c^-3//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+-1//3*b^2*c^-3//2*arctan(x*c^(1/2))*log(1+c*x^2)+-1//3*b^2*c^-3//2*arctanh(x*c^(1/2))*log(1+c*x^2)+-1//6*b^2*x^3*log(1+c*x^2)*log(1+-1*c*x^2)+1//3*a*b*x^3*log(1+c*x^2)+1//3*b^2*c^-3//2*arctan(x*c^(1/2))*log(1+-1*c*x^2)+1//3*b^2*c^-3//2*arctanh(x*c^(1/2))*log(-2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+1//3*b^2*c^-3//2*arctanh(x*c^(1/2))*log(2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+1//6*im*b^2*c^-3//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+1//6*im*b^2*c^-3//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+2//3*x*b^2*c^-1*log(1+c*x^2)+2//3*b^2*c^-3//2*arctan(x*c^(1/2))*log(2*(1+-1*im*x*c^(1/2))^-1)+2//3*b^2*c^-3//2*arctanh(x*c^(1/2))*log(2*(1+-1*x*c^(1/2))^-1)+4//3*a*b*x*c^-1)
@test integrate((a+b*arctanh(c*x^2))^2, x) == :(x*a^2+b^2*c^-1//2*Polylogarithms.polylog(2,1+-2*(1+x*c^(1/2))^-1)+b^2*c^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*x*c^(1/2))^-1)+-1*b^2*c^-1//2*arctanh(x*c^(1/2))^2+-1//2*b^2*c^-1//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+-1//2*b^2*c^-1//2*Polylogarithms.polylog(2,1+2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+1//4*x*b^2*log(1+c*x^2)^2+1//4*x*b^2*log(1+-1*c*x^2)^2+im*b^2*c^-1//2*arctan(x*c^(1/2))^2+im*b^2*c^-1//2*Polylogarithms.polylog(2,1+-2*(1+im*x*c^(1/2))^-1)+im*b^2*c^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*x*c^(1/2))^-1)+a*b*x*log(1+c*x^2)+b^2*c^-1//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+b^2*c^-1//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+b^2*c^-1//2*arctan(x*c^(1/2))*log(1+c*x^2)+b^2*c^-1//2*arctanh(x*c^(1/2))*log(-2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+b^2*c^-1//2*arctanh(x*c^(1/2))*log(2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+b^2*c^-1//2*arctanh(x*c^(1/2))*log(1+-1*c*x^2)+-1*a*b*x*log(1+-1*c*x^2)+-1*b^2*c^-1//2*arctan(x*c^(1/2))*log(1+-1*c*x^2)+-1*b^2*c^-1//2*arctanh(x*c^(1/2))*log(1+c*x^2)+-2*a*b*c^-1//2*arctanh(x*c^(1/2))+-2*b^2*c^-1//2*arctan(x*c^(1/2))*log(2*(1+-1*im*x*c^(1/2))^-1)+-2*b^2*c^-1//2*arctanh(x*c^(1/2))*log(2*(1+x*c^(1/2))^-1)+2*a*b*c^-1//2*arctan(x*c^(1/2))+2*b^2*c^-1//2*arctan(x*c^(1/2))*log(2*(1+im*x*c^(1/2))^-1)+2*b^2*c^-1//2*arctanh(x*c^(1/2))*log(2*(1+-1*x*c^(1/2))^-1)+-1//2*im*b^2*c^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+-1//2*im*b^2*c^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+-1//2*x*b^2*log(1+c*x^2)*log(1+-1*c*x^2))
@test integrate(x^-2*(a+b*arctanh(c*x^2))^2, x) == :(-1//4*x^-1*(2a+-1*b*log(1+-1*c*x^2))^2+b^2*c^(1/2)*arctanh(x*c^(1/2))^2+(1/2)*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+(1/2)*b^2*c^(1/2)*Polylogarithms.polylog(2,1+2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+-1*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-2*(1+x*c^(1/2))^-1)+-1*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-2*(1+-1*x*c^(1/2))^-1)+-1//4*b^2*x^-1*log(1+c*x^2)^2+im*b^2*c^(1/2)*arctan(x*c^(1/2))^2+im*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-2*(1+im*x*c^(1/2))^-1)+im*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-2*(1+-1*im*x*c^(1/2))^-1)+b*c^(1/2)*(2a+-1*b*log(1+-1*c*x^2))*arctanh(x*c^(1/2))+b^2*c^(1/2)*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+b^2*c^(1/2)*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+b^2*c^(1/2)*arctan(x*c^(1/2))*log(1+c*x^2)+b^2*c^(1/2)*arctanh(x*c^(1/2))*log(1+c*x^2)+(1/2)*b^2*x^-1*log(1+c*x^2)*log(1+-1*c*x^2)+-1*a*b*x^-1*log(1+c*x^2)+-1*b^2*c^(1/2)*arctan(x*c^(1/2))*log(1+-1*c*x^2)+-1*b^2*c^(1/2)*arctanh(x*c^(1/2))*log(-2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+-1*b^2*c^(1/2)*arctanh(x*c^(1/2))*log(2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+-2*b^2*c^(1/2)*arctan(x*c^(1/2))*log(2*(1+-1*im*x*c^(1/2))^-1)+-2*b^2*c^(1/2)*arctanh(x*c^(1/2))*log(2*(1+-1*x*c^(1/2))^-1)+2*a*b*c^(1/2)*arctan(x*c^(1/2))+2*b^2*c^(1/2)*arctan(x*c^(1/2))*log(2*(1+im*x*c^(1/2))^-1)+2*b^2*c^(1/2)*arctanh(x*c^(1/2))*log(2*(1+x*c^(1/2))^-1)+-1//2*im*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+-1//2*im*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2))))
@test integrate(x^-4*(a+b*arctanh(c*x^2))^2, x) == :(-1//12*x^-3*(2a+-1*b*log(1+-1*c*x^2))^2+-1//3*b^2*c^3//2*Polylogarithms.polylog(2,1+-2*(1+x*c^(1/2))^-1)+-1//3*b^2*c^3//2*Polylogarithms.polylog(2,1+-2*(1+-1*x*c^(1/2))^-1)+-1//12*b^2*x^-3*log(1+c*x^2)^2+1//3*b^2*c^3//2*arctanh(x*c^(1/2))^2+1//6*b^2*c^3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+1//6*b^2*c^3//2*Polylogarithms.polylog(2,1+2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+4//3*b^2*c^3//2*arctan(x*c^(1/2))+4//3*b^2*c^3//2*arctanh(x*c^(1/2))+-2//3*a*b*c*x^-1+-2//3*a*b*c^3//2*arctan(x*c^(1/2))+-2//3*c*b^2*x^-1*log(1+c*x^2)+-2//3*b^2*c^3//2*arctan(x*c^(1/2))*log(2*(1+im*x*c^(1/2))^-1)+-2//3*b^2*c^3//2*arctanh(x*c^(1/2))*log(2*(1+-1*x*c^(1/2))^-1)+-1//3*im*b^2*c^3//2*arctan(x*c^(1/2))^2+-1//3*im*b^2*c^3//2*Polylogarithms.polylog(2,1+-2*(1+im*x*c^(1/2))^-1)+-1//3*im*b^2*c^3//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*x*c^(1/2))^-1)+-1//3*a*b*x^-3*log(1+c*x^2)+-1//3*b*c*x^-1*(2a+-1*b*log(1+-1*c*x^2))+-1//3*b^2*c^3//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+-1//3*b^2*c^3//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+-1//3*b^2*c^3//2*arctan(x*c^(1/2))*log(1+c*x^2)+-1//3*b^2*c^3//2*arctanh(x*c^(1/2))*log(-2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+-1//3*b^2*c^3//2*arctanh(x*c^(1/2))*log(2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+1//3*b*c^3//2*(2a+-1*b*log(1+-1*c*x^2))*arctanh(x*c^(1/2))+1//3*c*b^2*x^-1*log(1+-1*c*x^2)+1//3*b^2*c^3//2*arctan(x*c^(1/2))*log(1+-1*c*x^2)+1//3*b^2*c^3//2*arctanh(x*c^(1/2))*log(1+c*x^2)+1//6*im*b^2*c^3//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+1//6*im*b^2*c^3//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+1//6*b^2*x^-3*log(1+c*x^2)*log(1+-1*c*x^2)+2//3*b^2*c^3//2*arctan(x*c^(1/2))*log(2*(1+-1*im*x*c^(1/2))^-1)+2//3*b^2*c^3//2*arctanh(x*c^(1/2))*log(2*(1+x*c^(1/2))^-1))
@test integrate(x^-6*(a+b*arctanh(c*x^2))^2, x) == :(-1//20*x^-5*(2a+-1*b*log(1+-1*c*x^2))^2+-8//15*b^2*c^2*x^-1+-4//15*b^2*c^5//2*arctan(x*c^(1/2))+-1//5*b^2*c^5//2*Polylogarithms.polylog(2,1+-2*(1+x*c^(1/2))^-1)+-1//5*b^2*c^5//2*Polylogarithms.polylog(2,1+-2*(1+-1*x*c^(1/2))^-1)+-1//20*b^2*x^-5*log(1+c*x^2)^2+1//5*b^2*c^5//2*arctanh(x*c^(1/2))^2+1//10*b^2*c^5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+1//10*b^2*c^5//2*Polylogarithms.polylog(2,1+2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+4//15*b^2*c^5//2*arctanh(x*c^(1/2))+-2//5*b^2*c^5//2*arctan(x*c^(1/2))*log(2*(1+-1*im*x*c^(1/2))^-1)+-2//5*b^2*c^5//2*arctanh(x*c^(1/2))*log(2*(1+-1*x*c^(1/2))^-1)+-2//15*a*b*c*x^-3+-2//15*c*b^2*x^-3*log(1+c*x^2)+-1//5*a*b*x^-5*log(1+c*x^2)+-1//5*b*c^2*x^-1*(2a+-1*b*log(1+-1*c*x^2))+-1//5*b^2*c^2*x^-1*log(1+-1*c*x^2)+-1//5*b^2*c^5//2*arctan(x*c^(1/2))*log(1+-1*c*x^2)+-1//5*b^2*c^5//2*arctanh(x*c^(1/2))*log(-2*c^(1/2)*(1+x*c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x*(-1c)^(1/2)))+-1//5*b^2*c^5//2*arctanh(x*c^(1/2))*log(2*c^(1/2)*(1+x*c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x*(-1c)^(1/2)))+-1//10*im*b^2*c^5//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+-1//10*im*b^2*c^5//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+-1//15*b*c*x^-3*(2a+-1*b*log(1+-1*c*x^2))+1//5*im*b^2*c^5//2*arctan(x*c^(1/2))^2+1//5*im*b^2*c^5//2*Polylogarithms.polylog(2,1+-2*(1+im*x*c^(1/2))^-1)+1//5*im*b^2*c^5//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*x*c^(1/2))^-1)+1//5*b*c^5//2*(2a+-1*b*log(1+-1*c*x^2))*arctanh(x*c^(1/2))+1//5*b^2*c^5//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+im)*(1+-1*x*c^(1/2)))+1//5*b^2*c^5//2*arctan(x*c^(1/2))*log((1+-1*im*x*c^(1/2))^-1*(1+-1im)*(1+x*c^(1/2)))+1//5*b^2*c^5//2*arctan(x*c^(1/2))*log(1+c*x^2)+1//5*b^2*c^5//2*arctanh(x*c^(1/2))*log(1+c*x^2)+1//10*b^2*x^-5*log(1+c*x^2)*log(1+-1*c*x^2)+1//15*c*b^2*x^-3*log(1+-1*c*x^2)+2//5*a*b*c^2*x^-1+2//5*a*b*c^5//2*arctan(x*c^(1/2))+2//5*b^2*c^5//2*arctan(x*c^(1/2))*log(2*(1+im*x*c^(1/2))^-1)+2//5*b^2*c^5//2*arctanh(x*c^(1/2))*log(2*(1+x*c^(1/2))^-1))
@test integrate(x^3*(a+b*arctanh(c*x^2))^3, x) == :(-1//4*c^-2*(a+b*arctanh(c*x^2))^3+1//4*x^4*(a+b*arctanh(c*x^2))^3+-3//4*b^3*c^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^2)^-1)+3//4*b*c^-2*(a+b*arctanh(c*x^2))^2+-3//2*b^2*c^-2*(a+b*arctanh(c*x^2))*log(2*(1+-1*c*x^2)^-1)+3//4*b*c^-1*x^2*(a+b*arctanh(c*x^2))^2)
@test integrate(x*(a+b*arctanh(c*x^2))^3, x) == :((1/2)*c^-1*(a+b*arctanh(c*x^2))^3+(1/2)*x^2*(a+b*arctanh(c*x^2))^3+3//4*b^3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^2)^-1)+-3//2*b*c^-1*(a+b*arctanh(c*x^2))^2*log(2*(1+-1*c*x^2)^-1)+-3//2*b^2*c^-1*(a+b*arctanh(c*x^2))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^2)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x^2))^3, x) == :((a+b*arctanh(c*x^2))^3*arctanh(1+-2*(1+-1*c*x^2)^-1)+-3//8*b^3*Polylogarithms.polylog(4,1+-2*(1+-1*c*x^2)^-1)+3//8*b^3*Polylogarithms.polylog(4,-1+2*(1+-1*c*x^2)^-1)+-3//4*b*(a+b*arctanh(c*x^2))^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^2)^-1)+-3//4*b^2*(a+b*arctanh(c*x^2))*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^2)^-1)+3//4*b*(a+b*arctanh(c*x^2))^2*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^2)^-1)+3//4*b^2*(a+b*arctanh(c*x^2))*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^2)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x^2))^3, x) == :((1/2)*c*(a+b*arctanh(c*x^2))^3+-1//2*x^-2*(a+b*arctanh(c*x^2))^3+-3//4*c*b^3*Polylogarithms.polylog(3,-1+2*(1+c*x^2)^-1)+-3//2*c*b^2*(a+b*arctanh(c*x^2))*Polylogarithms.polylog(2,-1+2*(1+c*x^2)^-1)+3//2*b*c*(a+b*arctanh(c*x^2))^2*log(2+-2*(1+c*x^2)^-1))
@test integrate(x^-5*(a+b*arctanh(c*x^2))^3, x) == :(-1//4*x^-4*(a+b*arctanh(c*x^2))^3+1//4*c^2*(a+b*arctanh(c*x^2))^3+-3//4*b^3*c^2*Polylogarithms.polylog(2,-1+2*(1+c*x^2)^-1)+3//4*b*c^2*(a+b*arctanh(c*x^2))^2+-3//4*b*c*x^-2*(a+b*arctanh(c*x^2))^2+3//2*b^2*c^2*(a+b*arctanh(c*x^2))*log(2+-2*(1+c*x^2)^-1))
@test integrate((d*x)^5//2*(a+b*arctanh(c*x^2)), x) == :(2//7*d^-1*(d*x)^7//2*(a+b*arctanh(c*x^2))+-2//7*b*c^-7//4*d^5//2*arctanh(c^1//4*d^-1//2*(d*x)^(1/2))+2//7*b*c^-7//4*d^5//2*arctan(c^1//4*d^-1//2*(d*x)^(1/2))+8//21*b*d*c^-1*(d*x)^3//2+-1//7*b*2^(1/2)*c^-7//4*d^5//2*arctan(1+2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+-1//14*b*2^(1/2)*c^-7//4*d^5//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+-1*2^(1/2)*c^1//4*(d*x)^(1/2))+1//7*b*2^(1/2)*c^-7//4*d^5//2*arctan(1+-1*2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+1//14*b*2^(1/2)*c^-7//4*d^5//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+2^(1/2)*c^1//4*(d*x)^(1/2)))
@test integrate((d*x)^3//2*(a+b*arctanh(c*x^2)), x) == :(2//5*d^-1*(d*x)^5//2*(a+b*arctanh(c*x^2))+-2//5*b*c^-5//4*d^3//2*arctan(c^1//4*d^-1//2*(d*x)^(1/2))+-2//5*b*c^-5//4*d^3//2*arctanh(c^1//4*d^-1//2*(d*x)^(1/2))+8//5*b*d*c^-1*(d*x)^(1/2)+-1//5*b*2^(1/2)*c^-5//4*d^3//2*arctan(1+2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+-1//10*b*2^(1/2)*c^-5//4*d^3//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+2^(1/2)*c^1//4*(d*x)^(1/2))+1//5*b*2^(1/2)*c^-5//4*d^3//2*arctan(1+-1*2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+1//10*b*2^(1/2)*c^-5//4*d^3//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+-1*2^(1/2)*c^1//4*(d*x)^(1/2)))
@test integrate((d*x)^(1/2)*(a+b*arctanh(c*x^2)), x) == :(2//3*d^-1*(d*x)^3//2*(a+b*arctanh(c*x^2))+-2//3*b*c^-3//4*d^(1/2)*arctanh(c^1//4*d^-1//2*(d*x)^(1/2))+2//3*b*c^-3//4*d^(1/2)*arctan(c^1//4*d^-1//2*(d*x)^(1/2))+-1//3*b*2^(1/2)*c^-3//4*d^(1/2)*arctan(1+-1*2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+-1//6*b*2^(1/2)*c^-3//4*d^(1/2)*log(d^(1/2)+x*c^(1/2)*d^(1/2)+2^(1/2)*c^1//4*(d*x)^(1/2))+1//3*b*2^(1/2)*c^-3//4*d^(1/2)*arctan(1+2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+1//6*b*2^(1/2)*c^-3//4*d^(1/2)*log(d^(1/2)+x*c^(1/2)*d^(1/2)+-1*2^(1/2)*c^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-1//2*(a+b*arctanh(c*x^2)), x) == :(2*d^-1*(d*x)^(1/2)*(a+b*arctanh(c*x^2))+-2*b*c^-1//4*d^-1//2*arctan(c^1//4*d^-1//2*(d*x)^(1/2))+-2*b*c^-1//4*d^-1//2*arctanh(c^1//4*d^-1//2*(d*x)^(1/2))+b*2^(1/2)*c^-1//4*d^-1//2*arctan(1+2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+(1/2)*b*2^(1/2)*c^-1//4*d^-1//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+2^(1/2)*c^1//4*(d*x)^(1/2))+-1*b*2^(1/2)*c^-1//4*d^-1//2*arctan(1+-1*2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+-1//2*b*2^(1/2)*c^-1//4*d^-1//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+-1*2^(1/2)*c^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-3//2*(a+b*arctanh(c*x^2)), x) == :(-1*d^-1*(d*x)^-1//2*(2a+2*b*arctanh(c*x^2))+-2*b*c^1//4*d^-3//2*arctan(c^1//4*d^-1//2*(d*x)^(1/2))+2*b*c^1//4*d^-3//2*arctanh(c^1//4*d^-1//2*(d*x)^(1/2))+b*2^(1/2)*c^1//4*d^-3//2*arctan(1+2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+(1/2)*b*2^(1/2)*c^1//4*d^-3//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+-1*2^(1/2)*c^1//4*(d*x)^(1/2))+-1*b*2^(1/2)*c^1//4*d^-3//2*arctan(1+-1*2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+-1//2*b*2^(1/2)*c^1//4*d^-3//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+2^(1/2)*c^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-5//2*(a+b*arctanh(c*x^2)), x) == :(-1//3*d^-1*(d*x)^-3//2*(2a+2*b*arctanh(c*x^2))+2//3*b*c^3//4*d^-5//2*arctan(c^1//4*d^-1//2*(d*x)^(1/2))+2//3*b*c^3//4*d^-5//2*arctanh(c^1//4*d^-1//2*(d*x)^(1/2))+-1//3*b*2^(1/2)*c^3//4*d^-5//2*arctan(1+-1*2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+-1//6*b*2^(1/2)*c^3//4*d^-5//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+-1*2^(1/2)*c^1//4*(d*x)^(1/2))+1//3*b*2^(1/2)*c^3//4*d^-5//2*arctan(1+2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+1//6*b*2^(1/2)*c^3//4*d^-5//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+2^(1/2)*c^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-7//2*(a+b*arctanh(c*x^2)), x) == :(-1//5*d^-1*(d*x)^-5//2*(2a+2*b*arctanh(c*x^2))+-8//5*b*c*d^-3*(d*x)^-1//2+-2//5*b*c^5//4*d^-7//2*arctan(c^1//4*d^-1//2*(d*x)^(1/2))+2//5*b*c^5//4*d^-7//2*arctanh(c^1//4*d^-1//2*(d*x)^(1/2))+-1//5*b*2^(1/2)*c^5//4*d^-7//2*arctan(1+2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+-1//10*b*2^(1/2)*c^5//4*d^-7//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+-1*2^(1/2)*c^1//4*(d*x)^(1/2))+1//5*b*2^(1/2)*c^5//4*d^-7//2*arctan(1+-1*2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+1//10*b*2^(1/2)*c^5//4*d^-7//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+2^(1/2)*c^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-9//2*(a+b*arctanh(c*x^2)), x) == :(-1//7*d^-1*(d*x)^-7//2*(2a+2*b*arctanh(c*x^2))+-8//21*b*c*d^-3*(d*x)^-3//2+2//7*b*c^7//4*d^-9//2*arctan(c^1//4*d^-1//2*(d*x)^(1/2))+2//7*b*c^7//4*d^-9//2*arctanh(c^1//4*d^-1//2*(d*x)^(1/2))+-1//7*b*2^(1/2)*c^7//4*d^-9//2*arctan(1+2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+-1//14*b*2^(1/2)*c^7//4*d^-9//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+2^(1/2)*c^1//4*(d*x)^(1/2))+1//7*b*2^(1/2)*c^7//4*d^-9//2*arctan(1+-1*2^(1/2)*c^1//4*d^-1//2*(d*x)^(1/2))+1//14*b*2^(1/2)*c^7//4*d^-9//2*log(d^(1/2)+x*c^(1/2)*d^(1/2)+-1*2^(1/2)*c^1//4*(d*x)^(1/2)))
@test integrate((d*x)^(1/2)*(a+b*arctanh(c*x^2))^2, x) == :(1//6*x*(d*x)^(1/2)*(2a+-1*b*log(1+-1*c*x^2))^2+-8//9*a*b*x*(d*x)^(1/2)+1//6*x*b^2*(d*x)^(1/2)*log(1+c*x^2)^2+4//9*b*x*(d*x)^(1/2)*(2a+-1*b*log(1+-1*c*x^2))+4//9*x*b^2*(d*x)^(1/2)*log(1+-1*c*x^2)+-2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))^2+-2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)^2+-1//3*x*b^2*(d*x)^(1/2)*log(1+c*x^2)*log(1+-1*c*x^2)+-1//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+-1//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+-1//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*(-1c)^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*(c^1//4+(-1c)^1//4)^-1*(1+c^1//4*x^(1/2)))+-1//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-1//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+-1//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*c^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+1//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+1//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*c^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+1//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+1//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*(-1c)^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2//3*a*b*x*(d*x)^(1/2)*log(1+c*x^2)+2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(1+c^1//4*x^(1/2))^-1)+2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(1+-1*c^1//4*x^(1/2))^-1)+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(1+x^(1/2)*(-1c)^1//4)^-1)+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(1+-1*x^(1/2)*(-1c)^1//4)^-1)+-4//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))*log(2*(1+im*c^1//4*x^(1/2))^-1)+-4//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))*log(2*(1+c^1//4*x^(1/2))^-1)+-4//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log(2*(1+im*x^(1/2)*(-1c)^1//4)^-1)+-4//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(1+x^(1/2)*(-1c)^1//4)^-1)+-2//3*im*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))^2+-2//3*im*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(1+im*c^1//4*x^(1/2))^-1)+-2//3*im*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(1+-1*im*c^1//4*x^(1/2))^-1)+-2//3*im*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)^2+-2//3*im*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(1+im*x^(1/2)*(-1c)^1//4)^-1)+-2//3*im*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1)+-2//3*b*c^-3//4*x^-1//2*(d*x)^(1/2)*(2a+-1*b*log(1+-1*c*x^2))*arctanh(c^1//4*x^(1/2))+-2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))*log(-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+-2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))*log(-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))*log(2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+-2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))*log(2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*c^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))*log(1+c*x^2)+-2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(-1*(-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*c^1//4)^-1*(1+c^1//4*x^(1/2)))+-2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*im*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+-2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log(1+c*x^2)+-2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*(-1c)^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(1+-1*c*x^2)+-1//3*im*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^1//4*x^(1/2))^-1*(1+im)*(1+-1*c^1//4*x^(1/2)))+-1//3*im*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^1//4*x^(1/2))^-1*(1+-1im)*(1+c^1//4*x^(1/2)))+-1//3*im*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-1*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+im)*(1+-1*x^(1/2)*(-1c)^1//4))+-1//3*im*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-1*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+-1im)*(1+x^(1/2)*(-1c)^1//4))+1//3*im*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+1//3*im*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+1//3*im*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+1//3*im*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*Polylogarithms.polylog(2,1+2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+1//3*im*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*c^1//4)^-1*(1+c^1//4*x^(1/2)))+1//3*im*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+1//3*im*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*im*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+1//3*im*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(-1*(-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+2//3*b*c^-3//4*x^-1//2*(d*x)^(1/2)*(2a+-1*b*log(1+-1*c*x^2))*arctan(c^1//4*x^(1/2))+2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))*log((1+-1*im*c^1//4*x^(1/2))^-1*(1+im)*(1+-1*c^1//4*x^(1/2)))+2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))*log((1+-1*im*c^1//4*x^(1/2))^-1*(1+-1im)*(1+c^1//4*x^(1/2)))+2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))*log(1+c*x^2)+2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*(-1c)^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+2//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log((1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+im)*(1+-1*x^(1/2)*(-1c)^1//4))+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log((1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+-1im)*(1+x^(1/2)*(-1c)^1//4))+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log(1+-1*c*x^2)+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*c^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*(c^1//4+(-1c)^1//4)^-1*(1+c^1//4*x^(1/2)))+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+2//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(1+c*x^2)+4//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(c^1//4*x^(1/2))*log(2*(1+-1*im*c^1//4*x^(1/2))^-1)+4//3*b^2*c^-3//4*x^-1//2*(d*x)^(1/2)*arctanh(c^1//4*x^(1/2))*log(2*(1+-1*c^1//4*x^(1/2))^-1)+4//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctan(x^(1/2)*(-1c)^1//4)*log(2*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1)+4//3*b^2*x^-1//2*(-1c)^-3//4*(d*x)^(1/2)*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(1+-1*x^(1/2)*(-1c)^1//4)^-1)+-2//3*a*b*2^(1/2)*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(1+-1*2^(1/2)*c^1//4*x^(1/2))+-1//3*a*b*2^(1/2)*c^-3//4*x^-1//2*(d*x)^(1/2)*log(1+x*c^(1/2)+2^(1/2)*c^1//4*x^(1/2))+1//3*a*b*2^(1/2)*c^-3//4*x^-1//2*(d*x)^(1/2)*log(1+x*c^(1/2)+-1*2^(1/2)*c^1//4*x^(1/2))+2//3*a*b*2^(1/2)*c^-3//4*x^-1//2*(d*x)^(1/2)*arctan(1+2^(1/2)*c^1//4*x^(1/2)))
@test integrate((d*x)^-1//2*(a+b*arctanh(c*x^2))^2, x) == :(2*x*a^2*(d*x)^-1//2+(1/2)*x*b^2*(d*x)^-1//2*log(1+c*x^2)^2+(1/2)*x*b^2*(d*x)^-1//2*log(1+-1*c*x^2)^2+b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*c^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*(-1c)^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1*x*b^2*(d*x)^-1//2*log(1+c*x^2)*log(1+-1*c*x^2)+-1*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+-1*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+-1*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*(-1c)^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*(c^1//4+(-1c)^1//4)^-1*(1+c^1//4*x^(1/2)))+-1*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-1*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+-1*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*c^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-2*a*b*x*(d*x)^-1//2*log(1+-1*c*x^2)+-2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))^2+-2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)^2+2*a*b*x*(d*x)^-1//2*log(1+c*x^2)+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+c^1//4*x^(1/2))^-1)+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*c^1//4*x^(1/2))^-1)+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+x^(1/2)*(-1c)^1//4)^-1)+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*x^(1/2)*(-1c)^1//4)^-1)+im*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^1//4*x^(1/2))^-1*(1+im)*(1+-1*c^1//4*x^(1/2)))+im*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^1//4*x^(1/2))^-1*(1+-1im)*(1+c^1//4*x^(1/2)))+im*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+im)*(1+-1*x^(1/2)*(-1c)^1//4))+im*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+-1im)*(1+x^(1/2)*(-1c)^1//4))+-1*im*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+-1*im*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1*im*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+-1*im*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1*im*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*c^1//4)^-1*(1+c^1//4*x^(1/2)))+-1*im*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-1*im*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*im*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+-1*im*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(-1*(-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-4*a*b*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))+-4*a*b*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))+-4*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*(1+-1*im*c^1//4*x^(1/2))^-1)+-4*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*(1+c^1//4*x^(1/2))^-1)+-4*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1)+-4*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(1+x^(1/2)*(-1c)^1//4)^-1)+-2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log((1+-1*im*c^1//4*x^(1/2))^-1*(1+im)*(1+-1*c^1//4*x^(1/2)))+-2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log((1+-1*im*c^1//4*x^(1/2))^-1*(1+-1im)*(1+c^1//4*x^(1/2)))+-2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(1+c*x^2)+-2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*c^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(1+c*x^2)+-2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log((1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+im)*(1+-1*x^(1/2)*(-1c)^1//4))+-2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log((1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+-1im)*(1+x^(1/2)*(-1c)^1//4))+-2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(1+-1*c*x^2)+-2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*(-1c)^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(1+-1*c*x^2)+2*im*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))^2+2*im*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+im*c^1//4*x^(1/2))^-1)+2*im*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c^1//4*x^(1/2))^-1)+2*im*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)^2+2*im*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+im*x^(1/2)*(-1c)^1//4)^-1)+2*im*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1)+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(1+-1*c*x^2)+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*(-1c)^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(1+-1*c*x^2)+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(-1*(-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*c^1//4)^-1*(1+c^1//4*x^(1/2)))+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*im*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(1+c*x^2)+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*c^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*(c^1//4+(-1c)^1//4)^-1*(1+c^1//4*x^(1/2)))+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+2*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(1+c*x^2)+4*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*(1+im*c^1//4*x^(1/2))^-1)+4*b^2*c^-1//4*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*(1+-1*c^1//4*x^(1/2))^-1)+4*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(1+im*x^(1/2)*(-1c)^1//4)^-1)+4*b^2*x^(1/2)*(-1c)^-1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(1+-1*x^(1/2)*(-1c)^1//4)^-1)+a*b*2^(1/2)*c^-1//4*x^(1/2)*(d*x)^-1//2*log(1+x*c^(1/2)+2^(1/2)*c^1//4*x^(1/2))+-1*a*b*2^(1/2)*c^-1//4*x^(1/2)*(d*x)^-1//2*log(1+x*c^(1/2)+-1*2^(1/2)*c^1//4*x^(1/2))+-2*a*b*2^(1/2)*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(1+-1*2^(1/2)*c^1//4*x^(1/2))+2*a*b*2^(1/2)*c^-1//4*x^(1/2)*(d*x)^-1//2*arctan(1+2^(1/2)*c^1//4*x^(1/2)))
@test integrate((d*x)^-3//2*(a+b*arctanh(c*x^2))^2, x) == :(-1//2*d^-1*(d*x)^-1//2*(2a+-1*b*log(1+-1*c*x^2))^2+-1//2*b^2*d^-1*(d*x)^-1//2*log(1+c*x^2)^2+b^2*d^-1*(d*x)^-1//2*log(1+c*x^2)*log(1+-1*c*x^2)+-2*a*b*d^-1*(d*x)^-1//2*log(1+c*x^2)+b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*(-1c)^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*(c^1//4+(-1c)^1//4)^-1*(1+c^1//4*x^(1/2)))+b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*c^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-1*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-1*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*c^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-1*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*(-1c)^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+c^1//4*x^(1/2))^-1)+-2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*c^1//4*x^(1/2))^-1)+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+x^(1/2)*(-1c)^1//4)^-1)+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*x^(1/2)*(-1c)^1//4)^-1)+2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))^2+2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)^2+im*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^1//4*x^(1/2))^-1*(1+im)*(1+-1*c^1//4*x^(1/2)))+im*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^1//4*x^(1/2))^-1*(1+-1im)*(1+c^1//4*x^(1/2)))+im*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+im)*(1+-1*x^(1/2)*(-1c)^1//4))+im*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+-1im)*(1+x^(1/2)*(-1c)^1//4))+-1*im*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+-1*im*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1*im*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+-1*im*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1*im*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*c^1//4)^-1*(1+c^1//4*x^(1/2)))+-1*im*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-1*im*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*im*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+-1*im*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(-1*(-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-4*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*(1+-1*im*c^1//4*x^(1/2))^-1)+-4*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*(1+-1*c^1//4*x^(1/2))^-1)+-4*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1)+-4*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(1+-1*x^(1/2)*(-1c)^1//4)^-1)+-2*b*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*(2a+-1*b*log(1+-1*c*x^2))*arctan(c^1//4*x^(1/2))+-2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log((1+-1*im*c^1//4*x^(1/2))^-1*(1+im)*(1+-1*c^1//4*x^(1/2)))+-2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log((1+-1*im*c^1//4*x^(1/2))^-1*(1+-1im)*(1+c^1//4*x^(1/2)))+-2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(1+c*x^2)+-2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+-2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*(-1c)^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+-2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log((1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+im)*(1+-1*x^(1/2)*(-1c)^1//4))+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log((1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+-1im)*(1+x^(1/2)*(-1c)^1//4))+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(1+-1*c*x^2)+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*c^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*(c^1//4+(-1c)^1//4)^-1*(1+c^1//4*x^(1/2)))+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+-2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(1+c*x^2)+2*im*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))^2+2*im*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+im*c^1//4*x^(1/2))^-1)+2*im*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c^1//4*x^(1/2))^-1)+2*im*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)^2+2*im*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+im*x^(1/2)*(-1c)^1//4)^-1)+2*im*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1)+2*b*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*(2a+-1*b*log(1+-1*c*x^2))*arctanh(c^1//4*x^(1/2))+2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*c^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+2*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(1+c*x^2)+2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(-1*(-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*c^1//4)^-1*(1+c^1//4*x^(1/2)))+2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*im*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(1+c*x^2)+2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*(-1c)^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(1+-1*c*x^2)+4*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*(1+im*c^1//4*x^(1/2))^-1)+4*b^2*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*(1+c^1//4*x^(1/2))^-1)+4*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(1+im*x^(1/2)*(-1c)^1//4)^-1)+4*b^2*d^-1*x^(1/2)*(-1c)^1//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(1+x^(1/2)*(-1c)^1//4)^-1)+a*b*2^(1/2)*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*log(1+x*c^(1/2)+-1*2^(1/2)*c^1//4*x^(1/2))+-1*a*b*2^(1/2)*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*log(1+x*c^(1/2)+2^(1/2)*c^1//4*x^(1/2))+-2*a*b*2^(1/2)*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(1+-1*2^(1/2)*c^1//4*x^(1/2))+2*a*b*2^(1/2)*c^1//4*d^-1*x^(1/2)*(d*x)^-1//2*arctan(1+2^(1/2)*c^1//4*x^(1/2)))
@test integrate((d*x)^-5//2*(a+b*arctanh(c*x^2))^2, x) == :(-1//6*d^-2*x^-1*(d*x)^-1//2*(2a+-1*b*log(1+-1*c*x^2))^2+-1//6*b^2*d^-2*x^-1*(d*x)^-1//2*log(1+c*x^2)^2+-2//3*a*b*d^-2*x^-1*(d*x)^-1//2*log(1+c*x^2)+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+c^1//4*x^(1/2))^-1)+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*c^1//4*x^(1/2))^-1)+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+x^(1/2)*(-1c)^1//4)^-1)+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*x^(1/2)*(-1c)^1//4)^-1)+-1//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-1//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*c^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-1//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-1//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*(-1c)^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+1//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+1//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+1//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+1//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*(-1c)^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+1//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*(c^1//4+(-1c)^1//4)^-1*(1+c^1//4*x^(1/2)))+1//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+1//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+1//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*c^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+1//3*b^2*d^-2*x^-1*(d*x)^-1//2*log(1+c*x^2)*log(1+-1*c*x^2)+2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))^2+2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)^2+-4//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*(1+im*c^1//4*x^(1/2))^-1)+-4//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*(1+-1*c^1//4*x^(1/2))^-1)+-4//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(1+im*x^(1/2)*(-1c)^1//4)^-1)+-4//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(1+-1*x^(1/2)*(-1c)^1//4)^-1)+-2//3*im*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))^2+-2//3*im*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+im*c^1//4*x^(1/2))^-1)+-2//3*im*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c^1//4*x^(1/2))^-1)+-2//3*im*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)^2+-2//3*im*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+im*x^(1/2)*(-1c)^1//4)^-1)+-2//3*im*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1)+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*(-1c)^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+-2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(-1*(-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*c^1//4)^-1*(1+c^1//4*x^(1/2)))+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*im*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(1+c*x^2)+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*c^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*(c^1//4+(-1c)^1//4)^-1*(1+c^1//4*x^(1/2)))+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+-2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(1+c*x^2)+-1//3*im*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^1//4*x^(1/2))^-1*(1+im)*(1+-1*c^1//4*x^(1/2)))+-1//3*im*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^1//4*x^(1/2))^-1*(1+-1im)*(1+c^1//4*x^(1/2)))+-1//3*im*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+im)*(1+-1*x^(1/2)*(-1c)^1//4))+-1//3*im*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+-1im)*(1+x^(1/2)*(-1c)^1//4))+1//3*im*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1c)^1//4)^-1*(1+x^(1/2)*(-1c)^1//4))+1//3*im*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+1//3*im*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1c)^1//4))+1//3*im*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*c^1//4*(1+-1*im*c^1//4*x^(1/2))^-1*(-1*c^1//4+im*(-1*(-1c)^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+1//3*im*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*c^1//4)^-1*(1+c^1//4*x^(1/2)))+1//3*im*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+1//3*im*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+-2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+-1*im*c^1//4)^-1*(1+-1*c^1//4*x^(1/2)))+1//3*im*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*Polylogarithms.polylog(2,1+2*(-1c)^1//4*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(-1*(-1c)^1//4+im*(-1*c^(1/2))^(1/2))^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+2//3*b*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*(2a+-1*b*log(1+-1*c*x^2))*arctan(c^1//4*x^(1/2))+2//3*b*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*(2a+-1*b*log(1+-1*c*x^2))*arctanh(c^1//4*x^(1/2))+2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log((1+-1*im*c^1//4*x^(1/2))^-1*(1+im)*(1+-1*c^1//4*x^(1/2)))+2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log((1+-1*im*c^1//4*x^(1/2))^-1*(1+-1im)*(1+c^1//4*x^(1/2)))+2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(1+c*x^2)+2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(-2*c^1//4*(1+c^1//4*x^(1/2))^-1*((-1*c^(1/2))^(1/2)+-1*c^1//4)^-1*(1+-1*x^(1/2)*(-1*c^(1/2))^(1/2)))+2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*c^1//4*(1+c^1//4*x^(1/2))^-1*(c^1//4+(-1*c^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*c^(1/2))^(1/2)))+2//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(1+c*x^2)+2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log((1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+im)*(1+-1*x^(1/2)*(-1c)^1//4))+2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log((1+-1*im*x^(1/2)*(-1c)^1//4)^-1*(1+-1im)*(1+x^(1/2)*(-1c)^1//4))+2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(1+-1*c*x^2)+2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(-2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1*(-1c)^(1/2))^(1/2)+-1*(-1c)^1//4)^-1*(1+-1*x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(-1c)^1//4*(1+x^(1/2)*(-1c)^1//4)^-1*((-1c)^1//4+(-1*(-1c)^(1/2))^(1/2))^-1*(1+x^(1/2)*(-1*(-1c)^(1/2))^(1/2)))+2//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(1+-1*c*x^2)+4//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(c^1//4*x^(1/2))*log(2*(1+-1*im*c^1//4*x^(1/2))^-1)+4//3*b^2*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctanh(c^1//4*x^(1/2))*log(2*(1+c^1//4*x^(1/2))^-1)+4//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctan(x^(1/2)*(-1c)^1//4)*log(2*(1+-1*im*x^(1/2)*(-1c)^1//4)^-1)+4//3*b^2*d^-2*x^(1/2)*(-1c)^3//4*(d*x)^-1//2*arctanh(x^(1/2)*(-1c)^1//4)*log(2*(1+x^(1/2)*(-1c)^1//4)^-1)+-2//3*a*b*2^(1/2)*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(1+-1*2^(1/2)*c^1//4*x^(1/2))+-1//3*a*b*2^(1/2)*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*log(1+x*c^(1/2)+-1*2^(1/2)*c^1//4*x^(1/2))+1//3*a*b*2^(1/2)*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*log(1+x*c^(1/2)+2^(1/2)*c^1//4*x^(1/2))+2//3*a*b*2^(1/2)*c^3//4*d^-2*x^(1/2)*(d*x)^-1//2*arctan(1+2^(1/2)*c^1//4*x^(1/2)))
@test integrate(x^11*(a+b*arctanh(c*x^3)), x) == :(1//12*x^12*(a+b*arctanh(c*x^3))+-1//12*b*c^-4*arctanh(c*x^3)+1//12*b*c^-3*x^3+1//36*b*c^-1*x^9)
@test integrate(x^8*(a+b*arctanh(c*x^3)), x) == :(1//9*x^9*(a+b*arctanh(c*x^3))+1//18*b*c^-1*x^6+1//18*b*c^-3*log(1+-1*c^2*x^6))
@test integrate(x^5*(a+b*arctanh(c*x^3)), x) == :(1//6*x^6*(a+b*arctanh(c*x^3))+-1//6*b*c^-2*arctanh(c*x^3)+1//6*b*c^-1*x^3)
@test integrate(x^2*(a+b*arctanh(c*x^3)), x) == :(1//3*x^3*(a+b*arctanh(c*x^3))+1//6*b*c^-1*log(1+-1*c^2*x^6))
@test integrate(x^-1*(a+b*arctanh(c*x^3)), x) == :(a*log(x)+-1//6*b*Polylogarithms.polylog(2,-1*c*x^3)+1//6*b*Polylogarithms.polylog(2,c*x^3))
@test integrate(x^-4*(a+b*arctanh(c*x^3)), x) == :(-1//3*x^-3*(a+b*arctanh(c*x^3))+b*c*log(x)+-1//6*b*c*log(1+-1*c^2*x^6))
@test integrate(x^-7*(a+b*arctanh(c*x^3)), x) == :(-1//6*x^-6*(a+b*arctanh(c*x^3))+-1//6*b*c*x^-3+1//6*b*c^2*arctanh(c*x^3))
@test integrate(x^-10*(a+b*arctanh(c*x^3)), x) == :(-1//9*x^-9*(a+b*arctanh(c*x^3))+-1//18*b*c*x^-6+-1//18*b*c^3*log(1+-1*c^2*x^6)+1//3*b*c^3*log(x))
@test integrate(x^3*(a+b*arctanh(c*x^3)), x) == :(1//4*x^4*(a+b*arctanh(c*x^3))+-1//4*b*c^-4//3*arctanh(x*c^1//3)+-1//16*b*c^-4//3*log(1+x*c^1//3+c^2//3*x^2)+1//16*b*c^-4//3*log(1+c^2//3*x^2+-1*x*c^1//3)+3//4*b*x*c^-1+-1//8*b*3^(1/2)*c^-4//3*arctan(1//3*3^(1/2)+2//3*x*3^(1/2)*c^1//3)+1//8*b*3^(1/2)*c^-4//3*arctan(1//3*3^(1/2)+-2//3*x*3^(1/2)*c^1//3))
@test integrate(a+b*arctanh(c*x^3), x) == :(a*x+b*x*arctanh(c*x^3)+(1/2)*b*c^-1//3*log(1+-1*c^2//3*x^2)+-1//4*b*c^-1//3*log(1+c^2//3*x^2+c^4//3*x^4)+(1/2)*b*3^(1/2)*c^-1//3*arctan(1//3*3^(1/2)*(1+2*c^2//3*x^2)))
@test integrate(x^-3*(a+b*arctanh(c*x^3)), x) == :(-1//2*x^-2*(a+b*arctanh(c*x^3))+(1/2)*b*c^2//3*arctanh(x*c^1//3)+-1//8*b*c^2//3*log(1+c^2//3*x^2+-1*x*c^1//3)+1//8*b*c^2//3*log(1+x*c^1//3+c^2//3*x^2)+-1//4*b*3^(1/2)*c^2//3*arctan(1//3*3^(1/2)+-2//3*x*3^(1/2)*c^1//3)+1//4*b*3^(1/2)*c^2//3*arctan(1//3*3^(1/2)+2//3*x*3^(1/2)*c^1//3))
@test integrate(x^-6*(a+b*arctanh(c*x^3)), x) == :(-1//5*x^-5*(a+b*arctanh(c*x^3))+-3//10*b*c*x^-2+-1//10*b*c^5//3*log(1+-1*c^2//3*x^2)+1//20*b*c^5//3*log(1+c^2//3*x^2+c^4//3*x^4)+-1//10*b*3^(1/2)*c^5//3*arctan(1//3*3^(1/2)*(1+2*c^2//3*x^2)))
@test integrate(x^7*(a+b*arctanh(c*x^3)), x) == :(1//8*x^8*(a+b*arctanh(c*x^3))+-1//8*b*c^-8//3*arctanh(x*c^1//3)+-1//32*b*c^-8//3*log(1+x*c^1//3+c^2//3*x^2)+1//32*b*c^-8//3*log(1+c^2//3*x^2+-1*x*c^1//3)+3//40*b*c^-1*x^5+-1//16*b*3^(1/2)*c^-8//3*arctan(1//3*3^(1/2)+-2//3*x*3^(1/2)*c^1//3)+1//16*b*3^(1/2)*c^-8//3*arctan(1//3*3^(1/2)+2//3*x*3^(1/2)*c^1//3))
@test integrate(x^4*(a+b*arctanh(c*x^3)), x) == :(1//5*x^5*(a+b*arctanh(c*x^3))+-1//20*b*c^-5//3*log(1+c^2//3*x^2+c^4//3*x^4)+1//10*b*c^-5//3*log(1+-1*c^2//3*x^2)+3//10*b*c^-1*x^2+-1//10*b*3^(1/2)*c^-5//3*arctan(1//3*3^(1/2)*(1+2*c^2//3*x^2)))
@test integrate(x*(a+b*arctanh(c*x^3)), x) == :((1/2)*x^2*(a+b*arctanh(c*x^3))+-1//2*b*c^-2//3*arctanh(x*c^1//3)+-1//8*b*c^-2//3*log(1+x*c^1//3+c^2//3*x^2)+1//8*b*c^-2//3*log(1+c^2//3*x^2+-1*x*c^1//3)+-1//4*b*3^(1/2)*c^-2//3*arctan(1//3*3^(1/2)+-2//3*x*3^(1/2)*c^1//3)+1//4*b*3^(1/2)*c^-2//3*arctan(1//3*3^(1/2)+2//3*x*3^(1/2)*c^1//3))
@test integrate(x^-2*(a+b*arctanh(c*x^3)), x) == :(-1*x^-1*(a+b*arctanh(c*x^3))+-1//2*b*c^1//3*log(1+-1*c^2//3*x^2)+1//4*b*c^1//3*log(1+c^2//3*x^2+c^4//3*x^4)+(1/2)*b*3^(1/2)*c^1//3*arctan(1//3*3^(1/2)*(1+2*c^2//3*x^2)))
@test integrate(x^-5*(a+b*arctanh(c*x^3)), x) == :(-1//4*x^-4*(a+b*arctanh(c*x^3))+-3//4*b*c*x^-1+-1//16*b*c^4//3*log(1+c^2//3*x^2+-1*x*c^1//3)+1//4*b*c^4//3*arctanh(x*c^1//3)+1//16*b*c^4//3*log(1+x*c^1//3+c^2//3*x^2)+-1//8*b*3^(1/2)*c^4//3*arctan(1//3*3^(1/2)+2//3*x*3^(1/2)*c^1//3)+1//8*b*3^(1/2)*c^4//3*arctan(1//3*3^(1/2)+-2//3*x*3^(1/2)*c^1//3))
@test integrate(x^11*(a+b*arctanh(c*x^3))^2, x) == :(-1//12*c^-4*(a+b*arctanh(c*x^3))^2+1//12*x^12*(a+b*arctanh(c*x^3))^2+1//9*b^2*c^-4*log(1+-1*c^2*x^6)+1//36*b^2*c^-2*x^6+1//6*a*b*c^-3*x^3+1//6*b^2*c^-3*x^3*arctanh(c*x^3)+1//18*b*c^-1*x^9*(a+b*arctanh(c*x^3)))
@test integrate(x^8*(a+b*arctanh(c*x^3))^2, x) == :(1//9*c^-3*(a+b*arctanh(c*x^3))^2+1//9*x^9*(a+b*arctanh(c*x^3))^2+-1//9*b^2*c^-3*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^3)^-1)+-1//9*b^2*c^-3*arctanh(c*x^3)+1//9*b^2*c^-2*x^3+-2//9*b*c^-3*(a+b*arctanh(c*x^3))*log(2*(1+-1*c*x^3)^-1)+1//9*b*c^-1*x^6*(a+b*arctanh(c*x^3)))
@test integrate(x^5*(a+b*arctanh(c*x^3))^2, x) == :(-1//6*c^-2*(a+b*arctanh(c*x^3))^2+1//6*x^6*(a+b*arctanh(c*x^3))^2+1//6*b^2*c^-2*log(1+-1*c^2*x^6)+1//3*a*b*c^-1*x^3+1//3*b^2*c^-1*x^3*arctanh(c*x^3))
@test integrate(x^2*(a+b*arctanh(c*x^3))^2, x) == :(1//3*c^-1*(a+b*arctanh(c*x^3))^2+1//3*x^3*(a+b*arctanh(c*x^3))^2+-1//3*b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^3)^-1)+-2//3*b*c^-1*(a+b*arctanh(c*x^3))*log(2*(1+-1*c*x^3)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x^3))^2, x) == :(-1//6*b^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^3)^-1)+1//6*b^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^3)^-1)+2//3*(a+b*arctanh(c*x^3))^2*arctanh(1+-2*(1+-1*c*x^3)^-1)+-1//3*b*(a+b*arctanh(c*x^3))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^3)^-1)+1//3*b*(a+b*arctanh(c*x^3))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^3)^-1))
@test integrate(x^-4*(a+b*arctanh(c*x^3))^2, x) == :(-1//3*x^-3*(a+b*arctanh(c*x^3))^2+1//3*c*(a+b*arctanh(c*x^3))^2+-1//3*c*b^2*Polylogarithms.polylog(2,-1+2*(1+c*x^3)^-1)+2//3*b*c*(a+b*arctanh(c*x^3))*log(2+-2*(1+c*x^3)^-1))
@test integrate(x^-7*(a+b*arctanh(c*x^3))^2, x) == :(-1//6*x^-6*(a+b*arctanh(c*x^3))^2+1//6*c^2*(a+b*arctanh(c*x^3))^2+b^2*c^2*log(x)+-1//6*b^2*c^2*log(1+-1*c^2*x^6)+-1//3*b*c*x^-3*(a+b*arctanh(c*x^3)))
@test integrate(x^-10*(a+b*arctanh(c*x^3))^2, x) == :(-1//9*x^-9*(a+b*arctanh(c*x^3))^2+1//9*c^3*(a+b*arctanh(c*x^3))^2+-1//9*b^2*c^2*x^-3+-1//9*b^2*c^3*Polylogarithms.polylog(2,-1+2*(1+c*x^3)^-1)+1//9*b^2*c^3*arctanh(c*x^3)+-1//9*b*c*x^-6*(a+b*arctanh(c*x^3))+2//9*b*c^3*(a+b*arctanh(c*x^3))*log(2+-2*(1+c*x^3)^-1))
@test integrate(x^8*(a+b*arctanh(c*x^3))^3, x) == :(1//9*c^-3*(a+b*arctanh(c*x^3))^3+1//9*x^9*(a+b*arctanh(c*x^3))^3+-1//6*b*c^-3*(a+b*arctanh(c*x^3))^2+1//6*b^3*c^-3*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^3)^-1)+1//6*b^3*c^-3*log(1+-1*c^2*x^6)+-1//3*b*c^-3*(a+b*arctanh(c*x^3))^2*log(2*(1+-1*c*x^3)^-1)+-1//3*b^2*c^-3*(a+b*arctanh(c*x^3))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^3)^-1)+1//3*a*b^2*c^-2*x^3+1//3*b^3*c^-2*x^3*arctanh(c*x^3)+1//6*b*c^-1*x^6*(a+b*arctanh(c*x^3))^2)
@test integrate(x^5*(a+b*arctanh(c*x^3))^3, x) == :(-1//6*c^-2*(a+b*arctanh(c*x^3))^3+1//6*x^6*(a+b*arctanh(c*x^3))^3+(1/2)*b*c^-2*(a+b*arctanh(c*x^3))^2+-1//2*b^3*c^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^3)^-1)+(1/2)*b*c^-1*x^3*(a+b*arctanh(c*x^3))^2+-1*b^2*c^-2*(a+b*arctanh(c*x^3))*log(2*(1+-1*c*x^3)^-1))
@test integrate(x^2*(a+b*arctanh(c*x^3))^3, x) == :(1//3*c^-1*(a+b*arctanh(c*x^3))^3+1//3*x^3*(a+b*arctanh(c*x^3))^3+(1/2)*b^3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^3)^-1)+-1*b*c^-1*(a+b*arctanh(c*x^3))^2*log(2*(1+-1*c*x^3)^-1)+-1*b^2*c^-1*(a+b*arctanh(c*x^3))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^3)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x^3))^3, x) == :(-1//4*b^3*Polylogarithms.polylog(4,1+-2*(1+-1*c*x^3)^-1)+1//4*b^3*Polylogarithms.polylog(4,-1+2*(1+-1*c*x^3)^-1)+2//3*(a+b*arctanh(c*x^3))^3*arctanh(1+-2*(1+-1*c*x^3)^-1)+(1/2)*b*(a+b*arctanh(c*x^3))^2*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^3)^-1)+(1/2)*b^2*(a+b*arctanh(c*x^3))*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^3)^-1)+-1//2*b*(a+b*arctanh(c*x^3))^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^3)^-1)+-1//2*b^2*(a+b*arctanh(c*x^3))*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^3)^-1))
@test integrate(x^-4*(a+b*arctanh(c*x^3))^3, x) == :(-1//3*x^-3*(a+b*arctanh(c*x^3))^3+1//3*c*(a+b*arctanh(c*x^3))^3+-1//2*c*b^3*Polylogarithms.polylog(3,-1+2*(1+c*x^3)^-1)+b*c*(a+b*arctanh(c*x^3))^2*log(2+-2*(1+c*x^3)^-1)+-1*c*b^2*(a+b*arctanh(c*x^3))*Polylogarithms.polylog(2,-1+2*(1+c*x^3)^-1))
@test integrate(x^-7*(a+b*arctanh(c*x^3))^3, x) == :(-1//6*x^-6*(a+b*arctanh(c*x^3))^3+1//6*c^2*(a+b*arctanh(c*x^3))^3+(1/2)*b*c^2*(a+b*arctanh(c*x^3))^2+-1//2*b^3*c^2*Polylogarithms.polylog(2,-1+2*(1+c*x^3)^-1)+b^2*c^2*(a+b*arctanh(c*x^3))*log(2+-2*(1+c*x^3)^-1)+-1//2*b*c*x^-3*(a+b*arctanh(c*x^3))^2)
@test integrate(x^3*(a+b*arctanh(c*x^-1)), x) == :(1//4*x^4*(a+b*arctanh(c*x^-1))+-1//4*b*c^4*arctanh(x*c^-1)+1//4*b*x*c^3+1//12*b*c*x^3)
@test integrate(x^2*(a+b*arctanh(c*x^-1)), x) == :(1//3*x^3*(a+b*arctanh(c*x^-1))+1//6*b*c*x^2+1//6*b*c^3*log(c^2+-1*x^2))
@test integrate(x*(a+b*arctanh(c*x^-1)), x) == :((1/2)*x^2*(a+b*arctanh(c*x^-1))+(1/2)*b*c*x+-1//2*b*c^2*arctanh(x*c^-1))
@test integrate(a+b*arctanh(c*x^-1), x) == :(a*x+b*x*arctanh(c*x^-1)+(1/2)*b*c*log(c^2+-1*x^2))
@test integrate(x^-1*(a+b*arctanh(c*x^-1)), x) == :(a*log(x)+(1/2)*b*Polylogarithms.polylog(2,-1*c*x^-1)+-1//2*b*Polylogarithms.polylog(2,c*x^-1))
@test integrate(x^-2*(a+b*arctanh(c*x^-1)), x) == :(-1*x^-1*(a+b*arctanh(c*x^-1))+-1//2*b*c^-1*log(1+-1*c^2*x^-2))
@test integrate(x^-3*(a+b*arctanh(c*x^-1)), x) == :(-1//2*x^-2*(a+b*arctanh(c*x^-1))+(1/2)*b*c^-2*arctanh(x*c^-1)+-1//2*b*c^-1*x^-1)
@test integrate(x^-4*(a+b*arctanh(c*x^-1)), x) == :(-1//3*x^-3*(a+b*arctanh(c*x^-1))+-1//6*b*c^-1*x^-2+-1//6*b*c^-3*log(c^2+-1*x^2)+1//3*b*c^-3*log(x))
@test integrate(x^3*(a+b*arctanh(c*x^-1))^2, x) == :(-1//4*c^4*(a+b*arccoth(x*c^-1))^2+1//4*x^4*(a+b*arccoth(x*c^-1))^2+1//3*b^2*c^4*log(1+-1*c^2*x^-2)+1//12*b^2*c^2*x^2+2//3*b^2*c^4*log(x)+(1/2)*b*x*c^3*(a+b*arccoth(x*c^-1))+1//6*b*c*x^3*(a+b*arccoth(x*c^-1)))
@test integrate(x^2*(a+b*arctanh(c*x^-1))^2, x) == :(-1//3*c^3*(a+b*arccoth(x*c^-1))^2+1//3*x^3*(a+b*arccoth(x*c^-1))^2+-1//3*b^2*c^3*arccoth(x*c^-1)+1//3*x*b^2*c^2+1//3*b^2*c^3*Polylogarithms.polylog(2,-1+2*(1+c*x^-1)^-1)+-2//3*b*c^3*(a+b*arccoth(x*c^-1))*log(2+-2*(1+c*x^-1)^-1)+1//3*b*c*x^2*(a+b*arccoth(x*c^-1)))
@test integrate(x*(a+b*arctanh(c*x^-1))^2, x) == :((1/2)*x^2*(a+b*arccoth(x*c^-1))^2+-1//2*c^2*(a+b*arccoth(x*c^-1))^2+b^2*c^2*log(x)+(1/2)*b^2*c^2*log(1+-1*c^2*x^-2)+b*c*x*(a+b*arccoth(x*c^-1)))
@test integrate((a+b*arctanh(c*x^-1))^2, x) == :(c*(a+b*arccoth(x*c^-1))^2+x*(a+b*arccoth(x*c^-1))^2+-1*c*b^2*Polylogarithms.polylog(2,-1*(c+-1x)^-1*(c+x))+-2*b*c*(a+b*arccoth(x*c^-1))*log(2*c*(c+-1x)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x^-1))^2, x) == :((1/2)*b^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^-1)^-1)+-2*(a+b*arccoth(x*c^-1))^2*arctanh(1+-2*(1+-1*c*x^-1)^-1)+-1//2*b^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^-1)^-1)+b*(a+b*arccoth(x*c^-1))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^-1)^-1)+-1*b*(a+b*arccoth(x*c^-1))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^-1)^-1))
@test integrate(x^-2*(a+b*arctanh(c*x^-1))^2, x) == :(-1*c^-1*(a+b*arccoth(x*c^-1))^2+-1*x^-1*(a+b*arccoth(x*c^-1))^2+b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^-1)^-1)+2*b*c^-1*(a+b*arccoth(x*c^-1))*log(2*(1+-1*c*x^-1)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x^-1))^2, x) == :((1/2)*c^-2*(a+b*arccoth(x*c^-1))^2+-1//2*x^-2*(a+b*arccoth(x*c^-1))^2+-1//2*b^2*c^-2*log(1+-1*c^2*x^-2)+-1*a*b*c^-1*x^-1+-1*b^2*c^-1*x^-1*arccoth(x*c^-1))
@test integrate(x^3*(a+b*arctanh(c*x^-1))^3, x) == :(-1//4*c^4*(a+b*arccoth(x*c^-1))^3+1//4*x^4*(a+b*arccoth(x*c^-1))^3+b^3*c^4*Polylogarithms.polylog(2,-1+2*(1+c*x^-1)^-1)+-1*b*c^4*(a+b*arccoth(x*c^-1))^2+-1//4*b^3*c^4*arccoth(x*c^-1)+1//4*x*b^3*c^3+-2*b^2*c^4*(a+b*arccoth(x*c^-1))*log(2+-2*(1+c*x^-1)^-1)+1//4*b*c*x^3*(a+b*arccoth(x*c^-1))^2+1//4*b^2*c^2*x^2*(a+b*arccoth(x*c^-1))+3//4*b*x*c^3*(a+b*arccoth(x*c^-1))^2)
@test integrate(x^2*(a+b*arctanh(c*x^-1))^3, x) == :(-1//3*c^3*(a+b*arccoth(x*c^-1))^3+1//3*x^3*(a+b*arccoth(x*c^-1))^3+b^3*c^3*log(x)+(1/2)*b^3*c^3*Polylogarithms.polylog(3,-1+2*(1+c*x^-1)^-1)+(1/2)*b^3*c^3*log(1+-1*c^2*x^-2)+-1//2*b*c^3*(a+b*arccoth(x*c^-1))^2+x*b^2*c^2*(a+b*arccoth(x*c^-1))+b^2*c^3*(a+b*arccoth(x*c^-1))*Polylogarithms.polylog(2,-1+2*(1+c*x^-1)^-1)+(1/2)*b*c*x^2*(a+b*arccoth(x*c^-1))^2+-1*b*c^3*(a+b*arccoth(x*c^-1))^2*log(2+-2*(1+c*x^-1)^-1))
@test integrate(x*(a+b*arctanh(c*x^-1))^3, x) == :((1/2)*x^2*(a+b*arccoth(x*c^-1))^3+-1//2*c^2*(a+b*arccoth(x*c^-1))^3+-3//2*b*c^2*(a+b*arccoth(x*c^-1))^2+3//2*b^3*c^2*Polylogarithms.polylog(2,-1+2*(1+c*x^-1)^-1)+-3*b^2*c^2*(a+b*arccoth(x*c^-1))*log(2+-2*(1+c*x^-1)^-1)+3//2*b*c*x*(a+b*arccoth(x*c^-1))^2)
@test integrate((a+b*arctanh(c*x^-1))^3, x) == :(c*(a+b*arccoth(x*c^-1))^3+x*(a+b*arccoth(x*c^-1))^3+3//2*c*b^3*Polylogarithms.polylog(3,1+-2*c*(c+-1x)^-1)+-3*b*c*(a+b*arccoth(x*c^-1))^2*log(2*c*(c+-1x)^-1)+-3*c*b^2*(a+b*arccoth(x*c^-1))*Polylogarithms.polylog(2,1+-2*c*(c+-1x)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x^-1))^3, x) == :(-2*(a+b*arccoth(x*c^-1))^3*arctanh(1+-2*(1+-1*c*x^-1)^-1)+-3//4*b^3*Polylogarithms.polylog(4,-1+2*(1+-1*c*x^-1)^-1)+3//4*b^3*Polylogarithms.polylog(4,1+-2*(1+-1*c*x^-1)^-1)+-3//2*b*(a+b*arccoth(x*c^-1))^2*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^-1)^-1)+-3//2*b^2*(a+b*arccoth(x*c^-1))*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^-1)^-1)+3//2*b*(a+b*arccoth(x*c^-1))^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^-1)^-1)+3//2*b^2*(a+b*arccoth(x*c^-1))*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^-1)^-1))
@test integrate(x^-2*(a+b*arctanh(c*x^-1))^3, x) == :(-1*c^-1*(a+b*arccoth(x*c^-1))^3+-1*x^-1*(a+b*arccoth(x*c^-1))^3+-3//2*b^3*c^-1*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^-1)^-1)+3*b*c^-1*(a+b*arccoth(x*c^-1))^2*log(2*(1+-1*c*x^-1)^-1)+3*b^2*c^-1*(a+b*arccoth(x*c^-1))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^-1)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x^-1))^3, x) == :((1/2)*c^-2*(a+b*arccoth(x*c^-1))^3+-1//2*x^-2*(a+b*arccoth(x*c^-1))^3+-3//2*b*c^-2*(a+b*arccoth(x*c^-1))^2+3//2*b^3*c^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^-1)^-1)+3*b^2*c^-2*(a+b*arccoth(x*c^-1))*log(2*(1+-1*c*x^-1)^-1)+-3//2*b*c^-1*x^-1*(a+b*arccoth(x*c^-1))^2)
@test integrate(x^7*(a+b*arctanh(c*x^-2)), x) == :(1//8*x^8*(a+b*arctanh(c*x^-2))+-1//8*b*c^4*arctanh(c^-1*x^2)+1//8*b*c^3*x^2+1//24*b*c*x^6)
@test integrate(x^5*(a+b*arctanh(c*x^-2)), x) == :(1//6*x^6*(a+b*arctanh(c*x^-2))+1//12*b*c*x^4+1//12*b*c^3*log(c^2+-1*x^4))
@test integrate(x^3*(a+b*arctanh(c*x^-2)), x) == :(1//4*x^4*(a+b*arctanh(c*x^-2))+-1//4*b*c^2*arctanh(c^-1*x^2)+1//4*b*c*x^2)
@test integrate(x*(a+b*arctanh(c*x^-2)), x) == :((1/2)*x^2*(a+b*arctanh(c*x^-2))+1//4*b*c*log(c^2+-1*x^4))
@test integrate(x^-1*(a+b*arctanh(c*x^-2)), x) == :(a*log(x)+-1//4*b*Polylogarithms.polylog(2,c*x^-2)+1//4*b*Polylogarithms.polylog(2,-1*c*x^-2))
@test integrate(x^-3*(a+b*arctanh(c*x^-2)), x) == :(-1//2*x^-2*(a+b*arctanh(c*x^-2))+-1//4*b*c^-1*log(1+-1*c^2*x^-4))
@test integrate(x^-5*(a+b*arctanh(c*x^-2)), x) == :(-1//4*x^-4*(a+b*arctanh(c*x^-2))+-1//4*b*c^-1*x^-2+1//4*b*c^-2*arctanh(c^-1*x^2))
@test integrate(x^-7*(a+b*arctanh(c*x^-2)), x) == :(-1//6*x^-6*(a+b*arctanh(c*x^-2))+-1//12*b*c^-1*x^-4+-1//12*b*c^-3*log(c^2+-1*x^4)+1//3*b*c^-3*log(x))
@test integrate(x^4*(a+b*arctanh(c*x^-2)), x) == :(1//5*x^5*(a+b*arctanh(c*x^-2))+-1//5*b*c^5//2*arctanh(x*c^-1//2)+1//5*b*c^5//2*arctan(x*c^-1//2)+2//15*b*c*x^3)
@test integrate(x^2*(a+b*arctanh(c*x^-2)), x) == :(1//3*x^3*(a+b*arctanh(c*x^-2))+-1//3*b*c^3//2*arctan(x*c^-1//2)+-1//3*b*c^3//2*arctanh(x*c^-1//2)+2//3*b*c*x)
@test integrate(a+b*arctanh(c*x^-2), x) == :(a*x+b*x*arctanh(c*x^-2)+b*c^(1/2)*arctan(x*c^-1//2)+-1*b*c^(1/2)*arctanh(x*c^-1//2))
@test integrate(x^-2*(a+b*arctanh(c*x^-2)), x) == :(-1*x^-1*(a+b*arctanh(c*x^-2))+b*c^-1//2*arctan(x*c^-1//2)+b*c^-1//2*arctanh(x*c^-1//2))
@test integrate(x^-4*(a+b*arctanh(c*x^-2)), x) == :(-1//3*x^-3*(a+b*arctanh(c*x^-2))+-2//3*b*c^-1*x^-1+-1//3*b*c^-3//2*arctan(x*c^-1//2)+1//3*b*c^-3//2*arctanh(x*c^-1//2))
@test integrate(x^-6*(a+b*arctanh(c*x^-2)), x) == :(-1//5*x^-5*(a+b*arctanh(c*x^-2))+-2//15*b*c^-1*x^-3+1//5*b*c^-5//2*arctan(x*c^-1//2)+1//5*b*c^-5//2*arctanh(x*c^-1//2))
@test integrate(x^3*(a+b*arctanh(c*x^-2))^2, x) == :(-1//4*c^2*(a+b*arccoth(c^-1*x^2))^2+1//4*x^4*(a+b*arccoth(c^-1*x^2))^2+b^2*c^2*log(x)+1//4*b^2*c^2*log(1+-1*c^2*x^-4)+(1/2)*b*c*x^2*(a+b*arccoth(c^-1*x^2)))
@test integrate(x*(a+b*arctanh(c*x^-2))^2, x) == :((1/2)*x^2*(a+b*arccoth(c^-1*x^2))^2+-1//2*c*(a+b*arccoth(c^-1*x^2))^2+(1/2)*c*b^2*Polylogarithms.polylog(2,-1+2*(1+c*x^-2)^-1)+-1*b*c*(a+b*arccoth(c^-1*x^2))*log(2+-2*(1+c*x^-2)^-1))
@test integrate(x^-1*(a+b*arctanh(c*x^-2))^2, x) == :(-1*(a+b*arccoth(c^-1*x^2))^2*arctanh(1+-2*(1+-1*c*x^-2)^-1)+-1//4*b^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^-2)^-1)+1//4*b^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^-2)^-1)+(1/2)*b*(a+b*arccoth(c^-1*x^2))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^-2)^-1)+-1//2*b*(a+b*arccoth(c^-1*x^2))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^-2)^-1))
@test integrate(x^-3*(a+b*arctanh(c*x^-2))^2, x) == :(-1//2*c^-1*(a+b*arccoth(c^-1*x^2))^2+-1//2*x^-2*(a+b*arccoth(c^-1*x^2))^2+(1/2)*b^2*c^-1*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^-2)^-1)+b*c^-1*(a+b*arccoth(c^-1*x^2))*log(2*(1+-1*c*x^-2)^-1))
@test integrate(x^-5*(a+b*arctanh(c*x^-2))^2, x) == :(-1//4*x^-4*(a+b*arccoth(c^-1*x^2))^2+1//4*c^-2*(a+b*arccoth(c^-1*x^2))^2+-1//4*b^2*c^-2*log(1+-1*c^2*x^-4)+-1//2*a*b*c^-1*x^-2+-1//2*b^2*c^-1*x^-2*arccoth(c^-1*x^2))
@test integrate(x^4*(a+b*arctanh(c*x^-2))^2, x) == :(1//20*x^5*(2a+-1*b*log(1+-1*c*x^-2))^2+-4//15*b^2*c^5//2*arctan(x*c^-1//2)+-4//15*b^2*c^5//2*arctanh(x*c^-1//2)+-1//5*b^2*c^5//2*Polylogarithms.polylog(2,x*c^-1//2)+-1//5*b^2*c^5//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(x+c^(1/2))^-1)+-1//10*b^2*c^5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+-1//10*b^2*c^5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+1//5*b^2*c^5//2*arctanh(x*c^-1//2)^2+1//5*b^2*c^5//2*Polylogarithms.polylog(2,-1*x*c^-1//2)+1//5*b^2*c^5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1)+1//20*b^2*x^5*log(1+c*x^-2)^2+8//15*x*b^2*c^2+-2//5*b^2*c^5//2*arctan(x*c^-1//2)*log(2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-2//5*b^2*c^5//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1)+-1//5*im*b^2*c^5//2*arctan(x*c^-1//2)^2+-1//5*im*b^2*c^5//2*Polylogarithms.polylog(2,-1*im*x*c^-1//2)+-1//5*im*b^2*c^5//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-1//5*b*c^5//2*(2a+-1*b*log(1+-1*c*x^-2))*arctanh(x*c^-1//2)+-1//5*b^2*c^5//2*arctan(x*c^-1//2)*log(1+-1*c*x^-2)+-1//5*b^2*c^5//2*arctanh(x*c^-1//2)*log(1+c*x^-2)+-1//10*im*b^2*c^5//2*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+-1//10*im*b^2*c^5//2*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+-1//10*b^2*x^5*log(1+c*x^-2)*log(1+-1*c*x^-2)+-1//15*c*b^2*x^3*log(1+-1*c*x^-2)+1//5*im*b^2*c^5//2*Polylogarithms.polylog(2,im*x*c^-1//2)+1//5*im*b^2*c^5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+1//5*a*b*x^5*log(1+c*x^-2)+1//5*b^2*c^5//2*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+1//5*b^2*c^5//2*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+1//5*b^2*c^5//2*arctan(x*c^-1//2)*log(1+c*x^-2)+1//5*b^2*c^5//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+1//5*b^2*c^5//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+1//15*b*c*x^3*(2a+-1*b*log(1+-1*c*x^-2))+2//5*a*b*c^5//2*arctan(x*c^-1//2)+2//5*b^2*c^5//2*arctan(x*c^-1//2)*log(2+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+2//5*b^2*c^5//2*arctanh(x*c^-1//2)*log(2+-2*c^(1/2)*(x+c^(1/2))^-1)+2//15*a*b*c*x^3+2//15*c*b^2*x^3*log(1+c*x^-2))
@test integrate(x^2*(a+b*arctanh(c*x^-2))^2, x) == :(1//12*x^3*(2a+-1*b*log(1+-1*c*x^-2))^2+-4//3*b^2*c^3//2*arctanh(x*c^-1//2)+-1//3*b^2*c^3//2*Polylogarithms.polylog(2,x*c^-1//2)+-1//3*b^2*c^3//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(x+c^(1/2))^-1)+-1//6*b^2*c^3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+-1//6*b^2*c^3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+1//3*b^2*c^3//2*arctanh(x*c^-1//2)^2+1//3*b^2*c^3//2*Polylogarithms.polylog(2,-1*x*c^-1//2)+1//3*b^2*c^3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1)+1//12*b^2*x^3*log(1+c*x^-2)^2+4//3*b^2*c^3//2*arctan(x*c^-1//2)+-2//3*a*b*c^3//2*arctan(x*c^-1//2)+-2//3*c*x*b^2*log(1+-1*c*x^-2)+-2//3*b^2*c^3//2*arctan(x*c^-1//2)*log(2+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-2//3*b^2*c^3//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1)+-1//3*im*b^2*c^3//2*Polylogarithms.polylog(2,im*x*c^-1//2)+-1//3*im*b^2*c^3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-1//3*b*c^3//2*(2a+-1*b*log(1+-1*c*x^-2))*arctanh(x*c^-1//2)+-1//3*b^2*c^3//2*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+-1//3*b^2*c^3//2*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+-1//3*b^2*c^3//2*arctan(x*c^-1//2)*log(1+c*x^-2)+-1//3*b^2*c^3//2*arctanh(x*c^-1//2)*log(1+c*x^-2)+-1//6*b^2*x^3*log(1+c*x^-2)*log(1+-1*c*x^-2)+1//3*im*b^2*c^3//2*arctan(x*c^-1//2)^2+1//3*im*b^2*c^3//2*Polylogarithms.polylog(2,-1*im*x*c^-1//2)+1//3*im*b^2*c^3//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+1//3*a*b*x^3*log(1+c*x^-2)+1//3*b^2*c^3//2*arctan(x*c^-1//2)*log(1+-1*c*x^-2)+1//3*b^2*c^3//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+1//3*b^2*c^3//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+1//6*im*b^2*c^3//2*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+1//6*im*b^2*c^3//2*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+2//3*c*x*b^2*log(1+c*x^-2)+2//3*b^2*c^3//2*arctan(x*c^-1//2)*log(2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+2//3*b^2*c^3//2*arctanh(x*c^-1//2)*log(2+-2*c^(1/2)*(x+c^(1/2))^-1)+4//3*a*b*c*x)
@test integrate((a+b*arctanh(c*x^-2))^2, x) == :(x*a^2+b^2*c^(1/2)*Polylogarithms.polylog(2,-1*x*c^-1//2)+b^2*c^(1/2)*Polylogarithms.polylog(2,1+x*c^-1//2)+b^2*c^(1/2)*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1)+b^2*(-1c)^(1/2)*Polylogarithms.polylog(2,1+x*(-1c)^-1//2)+(1/2)*b^2*c^(1/2)*Polylogarithms.polylog(2,1/2+-1//2*x*c^-1//2)+(1/2)*b^2*(-1c)^(1/2)*Polylogarithms.polylog(2,1/2+-1//2*x*(-1c)^-1//2)+-1*b^2*c^(1/2)*Polylogarithms.polylog(2,x*c^-1//2)+-1*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-1*x*c^-1//2)+-1*b^2*(-1c)^(1/2)*Polylogarithms.polylog(2,1+-1*x*(-1c)^-1//2)+-1//2*b^2*c^(1/2)*Polylogarithms.polylog(2,(1/2)*c^-1//2*(x+c^(1/2)))+-1//2*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+-1//2*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+-1//2*b^2*(-1c)^(1/2)*Polylogarithms.polylog(2,(1/2)*c^-1*(c+-1*x*(-1c)^(1/2)))+-1//4*b^2*c^(1/2)*log(x+c^(1/2))^2+-1//4*b^2*(-1c)^(1/2)*log(x+(-1c)^(1/2))^2+1//4*x*b^2*log(1+c*x^-2)^2+1//4*x*b^2*log(1+-1*c*x^-2)^2+1//4*b^2*c^(1/2)*log(c^(1/2)+-1x)^2+1//4*b^2*(-1c)^(1/2)*log((-1c)^(1/2)+-1x)^2+im*b^2*c^(1/2)*Polylogarithms.polylog(2,im*x*c^-1//2)+im*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+a*b*x*log(1+c*x^-2)+b^2*c^(1/2)*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+b^2*c^(1/2)*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+b^2*c^(1/2)*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+b^2*c^(1/2)*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+b^2*c^(1/2)*log(-1*x*c^-1//2)*log(x+c^(1/2))+b^2*(-1c)^(1/2)*log(-1*x*(-1c)^-1//2)*log(x+(-1c)^(1/2))+(1/2)*b^2*c^(1/2)*log((1/2)*c^-1//2*(x+c^(1/2)))*log(c^(1/2)+-1x)+(1/2)*b^2*c^(1/2)*log(1+-1*c*x^-2)*log(x+c^(1/2))+(1/2)*b^2*(-1c)^(1/2)*log((1/2)*(-1c)^-1//2*(x+(-1c)^(1/2)))*log((-1c)^(1/2)+-1x)+(1/2)*b^2*(-1c)^(1/2)*log(1+c*x^-2)*log(x+(-1c)^(1/2))+-1*im*b^2*c^(1/2)*Polylogarithms.polylog(2,-1*im*x*c^-1//2)+-1*a*b*x*log(1+-1*c*x^-2)+-1*b^2*c^(1/2)*arctan(x*c^-1//2)*log(1+-1*c*x^-2)+-1*b^2*c^(1/2)*arctanh(x*c^-1//2)*log(1+c*x^-2)+-1*b^2*c^(1/2)*log(x*c^-1//2)*log(c^(1/2)+-1x)+-1*b^2*(-1c)^(1/2)*log(x*(-1c)^-1//2)*log((-1c)^(1/2)+-1x)+-2*a*b*c^(1/2)*arctanh(x*c^-1//2)+-2*b^2*c^(1/2)*arctan(x*c^-1//2)*log(2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-2*b^2*c^(1/2)*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1)+2*a*b*c^(1/2)*arctan(x*c^-1//2)+-1//2*im*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+-1//2*im*b^2*c^(1/2)*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+-1//2*x*b^2*log(1+c*x^-2)*log(1+-1*c*x^-2)+-1//2*b^2*c^(1/2)*log((1/2)*c^-1//2*(c^(1/2)+-1x))*log(x+c^(1/2))+-1//2*b^2*c^(1/2)*log(1+-1*c*x^-2)*log(c^(1/2)+-1x)+-1//2*b^2*(-1c)^(1/2)*log((1/2)*(-1c)^-1//2*((-1c)^(1/2)+-1x))*log(x+(-1c)^(1/2))+-1//2*b^2*(-1c)^(1/2)*log(1+c*x^-2)*log((-1c)^(1/2)+-1x))
@test integrate(x^-2*(a+b*arctanh(c*x^-2))^2, x) == :(-1//4*x^-1*(2a+-1*b*log(1+-1*c*x^-2))^2+b^2*c^-1//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(x+c^(1/2))^-1)+(1/2)*b^2*c^-1//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(1+c^(1/2)*x^-1)^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x^-1*(-1c)^(1/2)))+(1/2)*b^2*c^-1//2*Polylogarithms.polylog(2,1+2*c^(1/2)*(1+c^(1/2)*x^-1)^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x^-1*(-1c)^(1/2)))+-1*b*x^-1*(2a+-1*b*log(1+-1*c*x^-2))+-1*b^2*c^-1//2*arctanh(x*c^-1//2)^2+-1*b^2*c^-1//2*Polylogarithms.polylog(2,1+-2*(1+c^(1/2)*x^-1)^-1)+-1*b^2*x^-1*log(1+-1*c*x^-2)+-2*b^2*c^-1//2*arccot(x*c^-1//2)+-2*b^2*c^-1//2*arccoth(x*c^-1//2)+-2*b^2*c^-1//2*arctan(x*c^-1//2)+2*a*b*x^-1+2*b^2*c^-1//2*arctanh(x*c^-1//2)+-1//4*b^2*x^-1*log(1+c*x^-2)^2+b*c^-1//2*(2a+-1*b*log(1+-1*c*x^-2))*arctanh(x*c^-1//2)+b^2*c^-1//2*arccot(x*c^-1//2)*log(1+-1*c*x^-2)+b^2*c^-1//2*arccoth(x*c^-1//2)*log(1+c*x^-2)+b^2*c^-1//2*arctan(x*c^-1//2)*log(1+c*x^-2)+(1/2)*im*b^2*c^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^(1/2)*x^-1)^-1*(1+im)*(1+-1*c^(1/2)*x^-1))+(1/2)*im*b^2*c^-1//2*Polylogarithms.polylog(2,1+-1*(1+-1*im*c^(1/2)*x^-1)^-1*(1+-1im)*(1+c^(1/2)*x^-1))+(1/2)*b^2*x^-1*log(1+c*x^-2)*log(1+-1*c*x^-2)+-1*im*b^2*c^-1//2*arctan(x*c^-1//2)^2+-1*im*b^2*c^-1//2*Polylogarithms.polylog(2,1+-2*(1+-1*im*c^(1/2)*x^-1)^-1)+-1*im*b^2*c^-1//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-1*a*b*x^-1*log(1+c*x^-2)+-1*b^2*c^-1//2*arccot(x*c^-1//2)*log((1+-1*im*c^(1/2)*x^-1)^-1*(1+im)*(1+-1*c^(1/2)*x^-1))+-1*b^2*c^-1//2*arccot(x*c^-1//2)*log((1+-1*im*c^(1/2)*x^-1)^-1*(1+-1im)*(1+c^(1/2)*x^-1))+-1*b^2*c^-1//2*arccoth(x*c^-1//2)*log(-2*c^(1/2)*(1+c^(1/2)*x^-1)^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*(1+-1*x^-1*(-1c)^(1/2)))+-1*b^2*c^-1//2*arccoth(x*c^-1//2)*log(2*c^(1/2)*(1+c^(1/2)*x^-1)^-1*(c^(1/2)+(-1c)^(1/2))^-1*(1+x^-1*(-1c)^(1/2)))+-2*a*b*c^-1//2*arccot(x*c^-1//2)+-2*b^2*c^-1//2*arctanh(x*c^-1//2)*log(2+-2*c^(1/2)*(x+c^(1/2))^-1)+2*b^2*c^-1//2*arccot(x*c^-1//2)*log(2*(1+-1*im*c^(1/2)*x^-1)^-1)+2*b^2*c^-1//2*arccoth(x*c^-1//2)*log(2*(1+c^(1/2)*x^-1)^-1)+2*b^2*c^-1//2*arctan(x*c^-1//2)*log(2+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1))
@test integrate(x^-4*(a+b*arctanh(c*x^-2))^2, x) == :(-1//12*x^-3*(2a+-1*b*log(1+-1*c*x^-2))^2+-1//3*b^2*c^-3//2*arctanh(x*c^-1//2)^2+-1//3*b^2*c^-3//2*Polylogarithms.polylog(2,-1*x*c^-1//2)+-1//3*b^2*c^-3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1)+-1//9*b*x^-3*(2a+-1*b*log(1+-1*c*x^-2))+-1//9*b^2*x^-3*log(1+-1*c*x^-2)+-1//12*b^2*x^-3*log(1+c*x^-2)^2+1//3*b^2*c^-3//2*Polylogarithms.polylog(2,x*c^-1//2)+1//3*b^2*c^-3//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(x+c^(1/2))^-1)+1//6*b^2*c^-3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+1//6*b^2*c^-3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+2//9*a*b*x^-3+4//3*b^2*c^-3//2*arctan(x*c^-1//2)+4//3*b^2*c^-3//2*arctanh(x*c^-1//2)+-2//3*a*b*c^-1*x^-1+-2//3*a*b*c^-3//2*arctan(x*c^-1//2)+-2//3*b^2*c^-1*x^-1*log(1+c*x^-2)+-2//3*b^2*c^-3//2*arctan(x*c^-1//2)*log(2+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-2//3*b^2*c^-3//2*arctanh(x*c^-1//2)*log(2+-2*c^(1/2)*(x+c^(1/2))^-1)+-1//3*im*b^2*c^-3//2*Polylogarithms.polylog(2,im*x*c^-1//2)+-1//3*im*b^2*c^-3//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-1//3*a*b*x^-3*log(1+c*x^-2)+-1//3*b*c^-1*x^-1*(2a+-1*b*log(1+-1*c*x^-2))+-1//3*b^2*c^-3//2*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+-1//3*b^2*c^-3//2*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+-1//3*b^2*c^-3//2*arctan(x*c^-1//2)*log(1+c*x^-2)+-1//3*b^2*c^-3//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+-1//3*b^2*c^-3//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+1//3*im*b^2*c^-3//2*arctan(x*c^-1//2)^2+1//3*im*b^2*c^-3//2*Polylogarithms.polylog(2,-1*im*x*c^-1//2)+1//3*im*b^2*c^-3//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+1//3*b*c^-3//2*(2a+-1*b*log(1+-1*c*x^-2))*arctanh(x*c^-1//2)+1//3*b^2*c^-1*x^-1*log(1+-1*c*x^-2)+1//3*b^2*c^-3//2*arctan(x*c^-1//2)*log(1+-1*c*x^-2)+1//3*b^2*c^-3//2*arctanh(x*c^-1//2)*log(1+c*x^-2)+1//6*im*b^2*c^-3//2*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+1//6*im*b^2*c^-3//2*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+1//6*b^2*x^-3*log(1+c*x^-2)*log(1+-1*c*x^-2)+2//3*b^2*c^-3//2*arctan(x*c^-1//2)*log(2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+2//3*b^2*c^-3//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1))
@test integrate(x^-6*(a+b*arctanh(c*x^-2))^2, x) == :(-1//20*x^-5*(2a+-1*b*log(1+-1*c*x^-2))^2+-8//15*b^2*c^-2*x^-1+-4//15*b^2*c^-5//2*arctan(x*c^-1//2)+-1//5*b^2*c^-5//2*arctanh(x*c^-1//2)^2+-1//5*b^2*c^-5//2*Polylogarithms.polylog(2,-1*x*c^-1//2)+-1//5*b^2*c^-5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1)+-1//20*b^2*x^-5*log(1+c*x^-2)^2+-1//25*b*x^-5*(2a+-1*b*log(1+-1*c*x^-2))+-1//25*b^2*x^-5*log(1+-1*c*x^-2)+1//5*b^2*c^-5//2*Polylogarithms.polylog(2,x*c^-1//2)+1//5*b^2*c^-5//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(x+c^(1/2))^-1)+1//10*b^2*c^-5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+1//10*b^2*c^-5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+2//25*a*b*x^-5+4//15*b^2*c^-5//2*arctanh(x*c^-1//2)+-2//5*b^2*c^-5//2*arctan(x*c^-1//2)*log(2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-2//5*b^2*c^-5//2*arctanh(x*c^-1//2)*log(2+-2*c^(1/2)*(x+c^(1/2))^-1)+-2//15*a*b*c^-1*x^-3+-2//15*b^2*c^-1*x^-3*log(1+c*x^-2)+-1//5*im*b^2*c^-5//2*arctan(x*c^-1//2)^2+-1//5*im*b^2*c^-5//2*Polylogarithms.polylog(2,-1*im*x*c^-1//2)+-1//5*im*b^2*c^-5//2*Polylogarithms.polylog(2,-1+2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+-1//5*a*b*x^-5*log(1+c*x^-2)+-1//5*b*c^-2*x^-1*(2a+-1*b*log(1+-1*c*x^-2))+-1//5*b^2*c^-2*x^-1*log(1+-1*c*x^-2)+-1//5*b^2*c^-5//2*arctan(x*c^-1//2)*log(1+-1*c*x^-2)+-1//5*b^2*c^-5//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*(c^(1/2)+(-1c)^(1/2))^-1*(x+(-1c)^(1/2)))+-1//5*b^2*c^-5//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1*((-1c)^(1/2)+-1*c^(1/2))^-1*((-1c)^(1/2)+-1x))+-1//10*im*b^2*c^-5//2*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+-1//10*im*b^2*c^-5//2*Polylogarithms.polylog(2,1+-1*(c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+-1//15*b*c^-1*x^-3*(2a+-1*b*log(1+-1*c*x^-2))+1//5*im*b^2*c^-5//2*Polylogarithms.polylog(2,im*x*c^-1//2)+1//5*im*b^2*c^-5//2*Polylogarithms.polylog(2,1+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+1//5*b*c^-5//2*(2a+-1*b*log(1+-1*c*x^-2))*arctanh(x*c^-1//2)+1//5*b^2*c^-5//2*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+im)*(c^(1/2)+-1x))+1//5*b^2*c^-5//2*arctan(x*c^-1//2)*log((c^(1/2)+-1*im*x)^-1*(1+-1im)*(x+c^(1/2)))+1//5*b^2*c^-5//2*arctan(x*c^-1//2)*log(1+c*x^-2)+1//5*b^2*c^-5//2*arctanh(x*c^-1//2)*log(1+c*x^-2)+1//10*b^2*x^-5*log(1+c*x^-2)*log(1+-1*c*x^-2)+1//15*b^2*c^-1*x^-3*log(1+-1*c*x^-2)+2//5*a*b*c^-2*x^-1+2//5*a*b*c^-5//2*arctan(x*c^-1//2)+2//5*b^2*c^-5//2*arctan(x*c^-1//2)*log(2+-2*c^(1/2)*(c^(1/2)+-1*im*x)^-1)+2//5*b^2*c^-5//2*arctanh(x*c^-1//2)*log(2*c^(1/2)*(x+c^(1/2))^-1))
@test integrate(x^3*(a+b*arctanh(c*x^(1/2))), x) == :(1//4*x^4*(a+b*arctanh(c*x^(1/2)))+-1//4*b*c^-8*arctanh(c*x^(1/2))+1//4*b*c^-7*x^(1/2)+1//12*b*c^-5*x^3//2+1//20*b*c^-3*x^5//2+1//28*b*c^-1*x^7//2)
@test integrate(x^2*(a+b*arctanh(c*x^(1/2))), x) == :(1//3*x^3*(a+b*arctanh(c*x^(1/2)))+-1//3*b*c^-6*arctanh(c*x^(1/2))+1//3*b*c^-5*x^(1/2)+1//9*b*c^-3*x^3//2+1//15*b*c^-1*x^5//2)
@test integrate(x*(a+b*arctanh(c*x^(1/2))), x) == :((1/2)*x^2*(a+b*arctanh(c*x^(1/2)))+(1/2)*b*c^-3*x^(1/2)+-1//2*b*c^-4*arctanh(c*x^(1/2))+1//6*b*c^-1*x^3//2)
@test integrate(a+b*arctanh(c*x^(1/2)), x) == :(a*x+b*x*arctanh(c*x^(1/2))+b*c^-1*x^(1/2)+-1*b*c^-2*arctanh(c*x^(1/2)))
@test integrate(x^-1*(a+b*arctanh(c*x^(1/2))), x) == :(a*log(x)+b*Polylogarithms.polylog(2,c*x^(1/2))+-1*b*Polylogarithms.polylog(2,-1*c*x^(1/2)))
@test integrate(x^-2*(a+b*arctanh(c*x^(1/2))), x) == :(-1*x^-1*(a+b*arctanh(c*x^(1/2)))+b*c^2*arctanh(c*x^(1/2))+-1*b*c*x^-1//2)
@test integrate(x^-3*(a+b*arctanh(c*x^(1/2))), x) == :(-1//2*x^-2*(a+b*arctanh(c*x^(1/2)))+(1/2)*b*c^4*arctanh(c*x^(1/2))+-1//2*b*c^3*x^-1//2+-1//6*b*c*x^-3//2)
@test integrate(x^-4*(a+b*arctanh(c*x^(1/2))), x) == :(-1//3*x^-3*(a+b*arctanh(c*x^(1/2)))+-1//3*b*c^5*x^-1//2+-1//9*b*c^3*x^-3//2+-1//15*b*c*x^-5//2+1//3*b*c^6*arctanh(c*x^(1/2)))
@test integrate(x^3*(a+b*arctanh(c*x^(1/2)))^2, x) == :(-1//4*c^-8*(a+b*arctanh(c*x^(1/2)))^2+1//4*x^4*(a+b*arctanh(c*x^(1/2)))^2+1//84*b^2*c^-2*x^3+3//70*b^2*c^-4*x^2+44//105*b^2*c^-8*log(1+-1*x*c^2)+71//420*x*b^2*c^-6+(1/2)*a*b*c^-7*x^(1/2)+(1/2)*b^2*c^-7*x^(1/2)*arctanh(c*x^(1/2))+1//6*b*c^-5*x^3//2*(a+b*arctanh(c*x^(1/2)))+1//10*b*c^-3*x^5//2*(a+b*arctanh(c*x^(1/2)))+1//14*b*c^-1*x^7//2*(a+b*arctanh(c*x^(1/2))))
@test integrate(x^2*(a+b*arctanh(c*x^(1/2)))^2, x) == :(-1//3*c^-6*(a+b*arctanh(c*x^(1/2)))^2+1//3*x^3*(a+b*arctanh(c*x^(1/2)))^2+1//30*b^2*c^-2*x^2+8//45*x*b^2*c^-4+23//45*b^2*c^-6*log(1+-1*x*c^2)+2//3*a*b*c^-5*x^(1/2)+2//3*b^2*c^-5*x^(1/2)*arctanh(c*x^(1/2))+2//9*b*c^-3*x^3//2*(a+b*arctanh(c*x^(1/2)))+2//15*b*c^-1*x^5//2*(a+b*arctanh(c*x^(1/2))))
@test integrate(x*(a+b*arctanh(c*x^(1/2)))^2, x) == :((1/2)*x^2*(a+b*arctanh(c*x^(1/2)))^2+-1//2*c^-4*(a+b*arctanh(c*x^(1/2)))^2+1//6*x*b^2*c^-2+2//3*b^2*c^-4*log(1+-1*x*c^2)+a*b*c^-3*x^(1/2)+b^2*c^-3*x^(1/2)*arctanh(c*x^(1/2))+1//3*b*c^-1*x^3//2*(a+b*arctanh(c*x^(1/2))))
@test integrate((a+b*arctanh(c*x^(1/2)))^2, x) == :(x*(a+b*arctanh(c*x^(1/2)))^2+-1*c^-2*(a+b*arctanh(c*x^(1/2)))^2+b^2*c^-2*log(1+-1*x*c^2)+2*a*b*c^-1*x^(1/2)+2*b^2*c^-1*x^(1/2)*arctanh(c*x^(1/2)))
@test integrate(x^-1*(a+b*arctanh(c*x^(1/2)))^2, x) == :(b^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^(1/2))^-1)+-1*b^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^(1/2))^-1)+4*(a+b*arctanh(c*x^(1/2)))^2*arctanh(1+-2*(1+-1*c*x^(1/2))^-1)+-2*b*(a+b*arctanh(c*x^(1/2)))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^(1/2))^-1)+2*b*(a+b*arctanh(c*x^(1/2)))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^(1/2))^-1))
@test integrate(x^-2*(a+b*arctanh(c*x^(1/2)))^2, x) == :(c^2*(a+b*arctanh(c*x^(1/2)))^2+-1*x^-1*(a+b*arctanh(c*x^(1/2)))^2+b^2*c^2*log(x)+-1*b^2*c^2*log(1+-1*x*c^2)+-2*b*c*x^-1//2*(a+b*arctanh(c*x^(1/2))))
@test integrate(x^-3*(a+b*arctanh(c*x^(1/2)))^2, x) == :((1/2)*c^4*(a+b*arctanh(c*x^(1/2)))^2+-1//2*x^-2*(a+b*arctanh(c*x^(1/2)))^2+-2//3*b^2*c^4*log(1+-1*x*c^2)+-1//6*b^2*c^2*x^-1+2//3*b^2*c^4*log(x)+-1*b*c^3*x^-1//2*(a+b*arctanh(c*x^(1/2)))+-1//3*b*c*x^-3//2*(a+b*arctanh(c*x^(1/2))))
@test integrate(x^3*(a+b*arctanh(c*x^(1/2)))^3, x) == :(-1//4*c^-8*(a+b*arctanh(c*x^(1/2)))^3+1//4*x^4*(a+b*arctanh(c*x^(1/2)))^3+-47//70*b^3*c^-8*arctanh(c*x^(1/2))+-44//35*b^3*c^-8*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^(1/2))^-1)+1//140*b^3*c^-3*x^5//2+23//420*b^3*c^-5*x^3//2+44//35*b*c^-8*(a+b*arctanh(c*x^(1/2)))^2+47//70*b^3*c^-7*x^(1/2)+-88//35*b^2*c^-8*(a+b*arctanh(c*x^(1/2)))*log(2*(1+-1*c*x^(1/2))^-1)+1//4*b*c^-5*x^3//2*(a+b*arctanh(c*x^(1/2)))^2+1//28*b^2*c^-2*x^3*(a+b*arctanh(c*x^(1/2)))+3//4*b*c^-7*x^(1/2)*(a+b*arctanh(c*x^(1/2)))^2+3//20*b*c^-3*x^5//2*(a+b*arctanh(c*x^(1/2)))^2+3//28*b*c^-1*x^7//2*(a+b*arctanh(c*x^(1/2)))^2+9//70*b^2*c^-4*x^2*(a+b*arctanh(c*x^(1/2)))+71//140*x*b^2*c^-6*(a+b*arctanh(c*x^(1/2))))
@test integrate(x^2*(a+b*arctanh(c*x^(1/2)))^3, x) == :(-1//3*c^-6*(a+b*arctanh(c*x^(1/2)))^3+1//3*x^3*(a+b*arctanh(c*x^(1/2)))^3+-23//15*b^3*c^-6*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^(1/2))^-1)+-19//30*b^3*c^-6*arctanh(c*x^(1/2))+1//30*b^3*c^-3*x^3//2+19//30*b^3*c^-5*x^(1/2)+23//15*b*c^-6*(a+b*arctanh(c*x^(1/2)))^2+b*c^-5*x^(1/2)*(a+b*arctanh(c*x^(1/2)))^2+-46//15*b^2*c^-6*(a+b*arctanh(c*x^(1/2)))*log(2*(1+-1*c*x^(1/2))^-1)+1//3*b*c^-3*x^3//2*(a+b*arctanh(c*x^(1/2)))^2+1//5*b*c^-1*x^5//2*(a+b*arctanh(c*x^(1/2)))^2+1//10*b^2*c^-2*x^2*(a+b*arctanh(c*x^(1/2)))+8//15*x*b^2*c^-4*(a+b*arctanh(c*x^(1/2))))
@test integrate(x*(a+b*arctanh(c*x^(1/2)))^3, x) == :((1/2)*x^2*(a+b*arctanh(c*x^(1/2)))^3+-1//2*c^-4*(a+b*arctanh(c*x^(1/2)))^3+(1/2)*b^3*c^-3*x^(1/2)+-2*b^3*c^-4*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^(1/2))^-1)+2*b*c^-4*(a+b*arctanh(c*x^(1/2)))^2+-1//2*b^3*c^-4*arctanh(c*x^(1/2))+(1/2)*b*c^-1*x^3//2*(a+b*arctanh(c*x^(1/2)))^2+(1/2)*x*b^2*c^-2*(a+b*arctanh(c*x^(1/2)))+-4*b^2*c^-4*(a+b*arctanh(c*x^(1/2)))*log(2*(1+-1*c*x^(1/2))^-1)+3//2*b*c^-3*x^(1/2)*(a+b*arctanh(c*x^(1/2)))^2)
@test integrate((a+b*arctanh(c*x^(1/2)))^3, x) == :(x*(a+b*arctanh(c*x^(1/2)))^3+-1*c^-2*(a+b*arctanh(c*x^(1/2)))^3+-3*b^3*c^-2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^(1/2))^-1)+3*b*c^-2*(a+b*arctanh(c*x^(1/2)))^2+-6*b^2*c^-2*(a+b*arctanh(c*x^(1/2)))*log(2*(1+-1*c*x^(1/2))^-1)+3*b*c^-1*x^(1/2)*(a+b*arctanh(c*x^(1/2)))^2)
@test integrate(x^-1*(a+b*arctanh(c*x^(1/2)))^3, x) == :(4*(a+b*arctanh(c*x^(1/2)))^3*arctanh(1+-2*(1+-1*c*x^(1/2))^-1)+-3//2*b^3*Polylogarithms.polylog(4,1+-2*(1+-1*c*x^(1/2))^-1)+3//2*b^3*Polylogarithms.polylog(4,-1+2*(1+-1*c*x^(1/2))^-1)+-3*b*(a+b*arctanh(c*x^(1/2)))^2*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^(1/2))^-1)+-3*b^2*(a+b*arctanh(c*x^(1/2)))*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^(1/2))^-1)+3*b*(a+b*arctanh(c*x^(1/2)))^2*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^(1/2))^-1)+3*b^2*(a+b*arctanh(c*x^(1/2)))*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^(1/2))^-1))
@test integrate(x^-2*(a+b*arctanh(c*x^(1/2)))^3, x) == :(c^2*(a+b*arctanh(c*x^(1/2)))^3+-1*x^-1*(a+b*arctanh(c*x^(1/2)))^3+-3*b^3*c^2*Polylogarithms.polylog(2,-1+2*(1+c*x^(1/2))^-1)+3*b*c^2*(a+b*arctanh(c*x^(1/2)))^2+-3*b*c*x^-1//2*(a+b*arctanh(c*x^(1/2)))^2+6*b^2*c^2*(a+b*arctanh(c*x^(1/2)))*log(2+-2*(1+c*x^(1/2))^-1))
@test integrate(x^-3*(a+b*arctanh(c*x^(1/2)))^3, x) == :((1/2)*c^4*(a+b*arctanh(c*x^(1/2)))^3+-1//2*x^-2*(a+b*arctanh(c*x^(1/2)))^3+(1/2)*b^3*c^4*arctanh(c*x^(1/2))+-2*b^3*c^4*Polylogarithms.polylog(2,-1+2*(1+c*x^(1/2))^-1)+2*b*c^4*(a+b*arctanh(c*x^(1/2)))^2+-1//2*b^3*c^3*x^-1//2+4*b^2*c^4*(a+b*arctanh(c*x^(1/2)))*log(2+-2*(1+c*x^(1/2))^-1)+-3//2*b*c^3*x^-1//2*(a+b*arctanh(c*x^(1/2)))^2+-1//2*b*c*x^-3//2*(a+b*arctanh(c*x^(1/2)))^2+-1//2*b^2*c^2*x^-1*(a+b*arctanh(c*x^(1/2))))
@test integrate(x^3//2*arctanh(x^(1/2)), x) == :(1//5*x+1//5*log(1+-1x)+1//10*x^2+2//5*x^5//2*arctanh(x^(1/2)))
@test integrate(x^(1/2)*arctanh(x^(1/2)), x) == :(1//3*x+1//3*log(1+-1x)+2//3*x^3//2*arctanh(x^(1/2)))
@test integrate(x^-1//2*arctanh(x^(1/2)), x) == :(2*x^(1/2)*arctanh(x^(1/2))+log(1+-1x))
@test integrate(x^-3//2*arctanh(x^(1/2)), x) == :(-1*log(1+-1x)+-2*x^-1//2*arctanh(x^(1/2))+log(x))
@test integrate(x^3*(a+b*arctanh(c*x^3//2)), x) == :(1//4*x^4*(a+b*arctanh(c*x^3//2))+-1//4*b*c^-8//3*arctanh(c^1//3*x^(1/2))+-1//16*b*c^-8//3*log(1+x*c^2//3+c^1//3*x^(1/2))+1//16*b*c^-8//3*log(1+x*c^2//3+-1*c^1//3*x^(1/2))+3//20*b*c^-1*x^5//2+-1//8*b*3^(1/2)*c^-8//3*arctan(1//3*3^(1/2)*(1+-2*c^1//3*x^(1/2)))+1//8*b*3^(1/2)*c^-8//3*arctan(1//3*3^(1/2)*(1+2*c^1//3*x^(1/2))))
@test integrate(x^2*(a+b*arctanh(c*x^3//2)), x) == :(1//3*x^3*(a+b*arctanh(c*x^3//2))+-1//3*b*c^-2*arctanh(c*x^3//2)+1//3*b*c^-1*x^3//2)
@test integrate(x*(a+b*arctanh(c*x^3//2)), x) == :((1/2)*x^2*(a+b*arctanh(c*x^3//2))+-1//2*b*c^-4//3*arctanh(c^1//3*x^(1/2))+-1//8*b*c^-4//3*log(1+x*c^2//3+c^1//3*x^(1/2))+1//8*b*c^-4//3*log(1+x*c^2//3+-1*c^1//3*x^(1/2))+3//2*b*c^-1*x^(1/2)+-1//4*b*3^(1/2)*c^-4//3*arctan(1//3*3^(1/2)*(1+2*c^1//3*x^(1/2)))+1//4*b*3^(1/2)*c^-4//3*arctan(1//3*3^(1/2)*(1+-2*c^1//3*x^(1/2))))
@test integrate(a+b*arctanh(c*x^3//2), x) == :(a*x+b*x*arctanh(c*x^3//2)+-1*b*c^-2//3*arctanh(c^1//3*x^(1/2))+-1//4*b*c^-2//3*log(1+x*c^2//3+c^1//3*x^(1/2))+1//4*b*c^-2//3*log(1+x*c^2//3+-1*c^1//3*x^(1/2))+(1/2)*b*3^(1/2)*c^-2//3*arctan(1//3*3^(1/2)*(1+2*c^1//3*x^(1/2)))+-1//2*b*3^(1/2)*c^-2//3*arctan(1//3*3^(1/2)*(1+-2*c^1//3*x^(1/2))))
@test integrate(x^-1*(a+b*arctanh(c*x^3//2)), x) == :(a*log(x)+-1//3*b*Polylogarithms.polylog(2,-1*c*x^3//2)+1//3*b*Polylogarithms.polylog(2,c*x^3//2))
@test integrate(x^-2*(a+b*arctanh(c*x^3//2)), x) == :(-1*x^-1*(a+b*arctanh(c*x^3//2))+b*c^2//3*arctanh(c^1//3*x^(1/2))+-1//4*b*c^2//3*log(1+x*c^2//3+-1*c^1//3*x^(1/2))+1//4*b*c^2//3*log(1+x*c^2//3+c^1//3*x^(1/2))+(1/2)*b*3^(1/2)*c^2//3*arctan(1//3*3^(1/2)*(1+2*c^1//3*x^(1/2)))+-1//2*b*3^(1/2)*c^2//3*arctan(1//3*3^(1/2)*(1+-2*c^1//3*x^(1/2))))
@test integrate(x^-3*(a+b*arctanh(c*x^3//2)), x) == :(-1//2*x^-2*(a+b*arctanh(c*x^3//2))+(1/2)*b*c^4//3*arctanh(c^1//3*x^(1/2))+-3//2*b*c*x^-1//2+-1//8*b*c^4//3*log(1+x*c^2//3+-1*c^1//3*x^(1/2))+1//8*b*c^4//3*log(1+x*c^2//3+c^1//3*x^(1/2))+-1//4*b*3^(1/2)*c^4//3*arctan(1//3*3^(1/2)*(1+2*c^1//3*x^(1/2)))+1//4*b*3^(1/2)*c^4//3*arctan(1//3*3^(1/2)*(1+-2*c^1//3*x^(1/2))))
@test integrate(x^-4*(a+b*arctanh(c*x^3//2)), x) == :(-1//3*x^-3*(a+b*arctanh(c*x^3//2))+-1//3*b*c*x^-3//2+1//3*b*c^2*arctanh(c*x^3//2))
@test integrate(x^2*(a+b*arctanh(c*x^3//2))^2, x) == :(-1//3*c^-2*(a+b*arctanh(c*x^3//2))^2+1//3*x^3*(a+b*arctanh(c*x^3//2))^2+1//3*b^2*c^-2*log(1+-1*c^2*x^3)+2//3*a*b*c^-1*x^3//2+2//3*b^2*c^-1*x^3//2*arctanh(c*x^3//2))
@test integrate(x^-1*(a+b*arctanh(c*x^3//2))^2, x) == :(-1//3*b^2*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^3//2)^-1)+1//3*b^2*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^3//2)^-1)+4//3*(a+b*arctanh(c*x^3//2))^2*arctanh(1+-2*(1+-1*c*x^3//2)^-1)+-2//3*b*(a+b*arctanh(c*x^3//2))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^3//2)^-1)+2//3*b*(a+b*arctanh(c*x^3//2))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^3//2)^-1))
@test integrate(x^-4*(a+b*arctanh(c*x^3//2))^2, x) == :(-1//3*x^-3*(a+b*arctanh(c*x^3//2))^2+1//3*c^2*(a+b*arctanh(c*x^3//2))^2+b^2*c^2*log(x)+-1//3*b^2*c^2*log(1+-1*c^2*x^3)+-2//3*b*c*x^-3//2*(a+b*arctanh(c*x^3//2)))
@test integrate(x^3*arctanh(c*x^3//2)^2, x) == :(-3//40*c^-8//3*log(1+x*c^2//3+c^1//3*x^(1/2))+-3//40*c^-8//3*log(1+x*c^2//3+-1*c^1//3*x^(1/2))+-1//8*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+-1//8*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//8*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+-1//8*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//8*c^-8//3*Polylogarithms.polylog(2,1/2+(1/2)*c^1//3*x^(1/2))+-1//8*c^-8//3*Polylogarithms.polylog(2,1/2+-1//2*c^1//3*x^(1/2))+1//8*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+1//8*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+1//8*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+1//8*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+1//16*c^-8//3*log(1+c^1//3*x^(1/2))^2+1//16*c^-8//3*log(1+-1*c^1//3*x^(1/2))^2+1//16*x^4*log(1+c*x^3//2)^2+1//16*x^4*log(1+-1*c*x^3//2)^2+3//20*c^-8//3*log(1+c^1//3*x^(1/2))+3//20*c^-8//3*log(1+-1*c^1//3*x^(1/2))+9//20*x*c^-2+-3//20*c^-1*x^5//2*log(1+-1*c*x^3//2)+-1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+-1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+-1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+-1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+-1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+-1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+-1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+-1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1+c^1//3*x^(1/2))+-1//8*c^-8//3*log((1+(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//8*c^-8//3*log((1+(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+-1//8*c^-8//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+-1//8*c^-8//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//8*c^-8//3*log(1+c*x^3//2)*log(1+c^1//3*x^(1/2))+-1//8*c^-8//3*log(1+c^1//3*x^(1/2))*log(1/2+-1//2*c^1//3*x^(1/2))+-1//8*c^-8//3*log(1+-1*c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+-1//8*c^-8//3*log(1+-1*c^1//3*x^(1/2))*log(1/2+(1/2)*c^1//3*x^(1/2))+-1//8*x^4*log(1+c*x^3//2)*log(1+-1*c*x^3//2)+-1//16*(-1)^1//3*c^-8//3*log(1+(-1)^1//3*c^1//3*x^(1/2))^2+-1//16*(-1)^1//3*c^-8//3*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))^2+1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+-1*c^1//3*x^(1/2))+1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+1//8*(-1)^2//3*c^-8//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//8*c^-8//3*log((1+(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+1//8*c^-8//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+1//8*c^-8//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+1//8*c^-8//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+1//8*c^-8//3*log(1+c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+1//8*c^-8//3*log(1+c^1//3*x^(1/2))*log(1+-1*c*x^3//2)+1//16*(-1)^2//3*c^-8//3*log(1+(-1)^2//3*c^1//3*x^(1/2))^2+1//16*(-1)^2//3*c^-8//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))^2+3//20*3^(1/2)*c^-8//3*arctan(1//3*3^(1/2)*(1+-2*c^1//3*x^(1/2)))+3//20*3^(1/2)*c^-8//3*arctan(1//3*3^(1/2)*(1+2*c^1//3*x^(1/2)))+3//20*c^-1*x^5//2*log(1+c*x^3//2)+-1//8*(-1)^1//3*c^-8//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+-1//8*(-1)^1//3*c^-8//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//8*(-1)^1//3*c^-8//3*log(-1*(-1)^1//3*(1+-1*(-1)^2//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//8*(-1)^1//3*c^-8//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+-1//8*(-1)^1//3*c^-8//3*log(1+c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//8*(-1)^1//3*c^-8//3*log(1+-1*c*x^3//2)*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*log((1+(-1)^1//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//8*(-1)^2//3*c^-8//3*log((1+(-1)^1//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+-1//8*(-1)^2//3*c^-8//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+(-1)^2//3*c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*log(1+c*x^3//2)*log(1+(-1)^2//3*c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*log(1+-1*c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*log(1+(-1)^2//3*c^1//3*x^(1/2))*log(1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*log(1+(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+-1//8*(-1)^2//3*c^-8//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+-1*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*log(1+c*x^3//2)*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*log(1+-1*c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log(1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+-1*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))*log(1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))+1//8*(-1)^1//3*c^-8//3*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+c^1//3*x^(1/2))+1//8*(-1)^2//3*c^-8//3*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//8*(-1)^2//3*c^-8//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))*log(1+(-1)^2//3*c^1//3*x^(1/2))+1//8*(-1)^2//3*c^-8//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(1+(-1)^2//3*c^1//3*x^(1/2))+1//8*(-1)^2//3*c^-8//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//8*(-1)^2//3*c^-8//3*log(1+c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//8*(-1)^2//3*c^-8//3*log(1+-1*c*x^3//2)*log(1+(-1)^2//3*c^1//3*x^(1/2)))
@test integrate(arctanh(c*x^3//2)^2, x) == :((1/2)*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+(1/2)*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+(1/2)*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+(1/2)*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//2*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+-1//2*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//2*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+-1//2*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//2*c^-2//3*Polylogarithms.polylog(2,1/2+(1/2)*c^1//3*x^(1/2))+-1//2*c^-2//3*Polylogarithms.polylog(2,1/2+-1//2*c^1//3*x^(1/2))+1//4*x*log(1+c*x^3//2)^2+1//4*x*log(1+-1*c*x^3//2)^2+1//4*c^-2//3*log(1+c^1//3*x^(1/2))^2+1//4*c^-2//3*log(1+-1*c^1//3*x^(1/2))^2+(1/2)*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+(1/2)*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+(1/2)*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+-1*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+(1/2)*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+(1/2)*c^-2//3*log((1+(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+(1/2)*c^-2//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+(1/2)*c^-2//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+(1/2)*c^-2//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+(1/2)*c^-2//3*log(1+c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+(1/2)*c^-2//3*log(1+c^1//3*x^(1/2))*log(1+-1*c*x^3//2)+-1//2*x*log(1+c*x^3//2)*log(1+-1*c*x^3//2)+-1//2*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+-1//2*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+-1//2*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+-1//2*(-1)^1//3*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1+c^1//3*x^(1/2))+-1//2*c^-2//3*log((1+(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//2*c^-2//3*log((1+(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+-1//2*c^-2//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+-1//2*c^-2//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//2*c^-2//3*log(1+c*x^3//2)*log(1+c^1//3*x^(1/2))+-1//2*c^-2//3*log(1+c^1//3*x^(1/2))*log(1/2+-1//2*c^1//3*x^(1/2))+-1//2*c^-2//3*log(1+-1*c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+-1//2*c^-2//3*log(1+-1*c^1//3*x^(1/2))*log(1/2+(1/2)*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^-2//3*log(1+(-1)^1//3*c^1//3*x^(1/2))^2+-1//4*(-1)^1//3*c^-2//3*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))^2+1//4*(-1)^2//3*c^-2//3*log(1+(-1)^2//3*c^1//3*x^(1/2))^2+1//4*(-1)^2//3*c^-2//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))^2+(1/2)*(-1)^1//3*c^-2//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*log(1+c*x^3//2)*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*log(1+-1*c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log(1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+-1*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))*log(1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^-2//3*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^-2//3*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^-2//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))*log(1+(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^-2//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(1+(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^-2//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^-2//3*log(1+c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^-2//3*log(1+-1*c*x^3//2)*log(1+(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^-2//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^-2//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^-2//3*log(-1*(-1)^1//3*(1+-1*(-1)^2//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^-2//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^-2//3*log(1+c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^-2//3*log(1+-1*c*x^3//2)*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*log((1+(-1)^1//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^-2//3*log((1+(-1)^1//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^-2//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*log(1+c*x^3//2)*log(1+(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*log(1+-1*c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*log(1+(-1)^2//3*c^1//3*x^(1/2))*log(1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*log(1+(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^-2//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+-1*c^1//3*x^(1/2)))
@test integrate(x^-3*arctanh(c*x^3//2)^2, x) == :(-3//2*c^4//3*log(1+c^1//3*x^(1/2))+-3//2*c^4//3*log(1+-1*c^1//3*x^(1/2))+-1//4*c^4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+-1//4*c^4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//4*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+-1//4*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//8*c^4//3*log(1+c^1//3*x^(1/2))^2+-1//8*c^4//3*log(1+-1*c^1//3*x^(1/2))^2+-1//8*x^-2*log(1+c*x^3//2)^2+-1//8*x^-2*log(1+-1*c*x^3//2)^2+1//4*c^4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+1//4*c^4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+1//4*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+1//4*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+1//4*c^4//3*Polylogarithms.polylog(2,1/2+(1/2)*c^1//3*x^(1/2))+1//4*c^4//3*Polylogarithms.polylog(2,1/2+-1//2*c^1//3*x^(1/2))+3//4*c^4//3*log(1+x*c^2//3+c^1//3*x^(1/2))+3//4*c^4//3*log(1+x*c^2//3+-1*c^1//3*x^(1/2))+-3//2*c*x^-1//2*log(1+c*x^3//2)+-3//2*3^(1/2)*c^4//3*arctan(1//3*3^(1/2)*(1+-2*c^1//3*x^(1/2)))+-3//2*3^(1/2)*c^4//3*arctan(1//3*3^(1/2)*(1+2*c^1//3*x^(1/2)))+-1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+-1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+-1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+-1*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+-1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//4*c^4//3*log((1+(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//4*c^4//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+-1//4*c^4//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+-1//4*c^4//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//4*c^4//3*log(1+c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+-1//4*c^4//3*log(1+c^1//3*x^(1/2))*log(1+-1*c*x^3//2)+-1//8*(-1)^2//3*c^4//3*log(1+(-1)^2//3*c^1//3*x^(1/2))^2+-1//8*(-1)^2//3*c^4//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))^2+1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+1//4*(-1)^1//3*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1+c^1//3*x^(1/2))+1//4*c^4//3*log((1+(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+1//4*c^4//3*log((1+(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+1//4*c^4//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+c^1//3*x^(1/2))+1//4*c^4//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+1//4*c^4//3*log(1+c*x^3//2)*log(1+c^1//3*x^(1/2))+1//4*c^4//3*log(1+c^1//3*x^(1/2))*log(1/2+-1//2*c^1//3*x^(1/2))+1//4*c^4//3*log(1+-1*c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+1//4*c^4//3*log(1+-1*c^1//3*x^(1/2))*log(1/2+(1/2)*c^1//3*x^(1/2))+1//4*x^-2*log(1+c*x^3//2)*log(1+-1*c*x^3//2)+1//8*(-1)^1//3*c^4//3*log(1+(-1)^1//3*c^1//3*x^(1/2))^2+1//8*(-1)^1//3*c^4//3*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))^2+3//2*c*x^-1//2*log(1+-1*c*x^3//2)+-1//4*(-1)^1//3*c^4//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*log(1+c*x^3//2)*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*log(1+-1*c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log(1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+-1*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))*log(1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^4//3*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^4//3*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^4//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))*log(1+(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^4//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(1+(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^4//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^4//3*log(1+c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^4//3*log(1+-1*c*x^3//2)*log(1+(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^4//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^4//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^4//3*log(-1*(-1)^1//3*(1+-1*(-1)^2//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^4//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^4//3*log(1+c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^4//3*log(1+-1*c*x^3//2)*log(1+-1*(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*log((1+(-1)^1//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^4//3*log((1+(-1)^1//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^4//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*log(1+c*x^3//2)*log(1+(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*log(1+-1*c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*log(1+(-1)^2//3*c^1//3*x^(1/2))*log(1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*log(1+(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^4//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+-1*c^1//3*x^(1/2)))
@test integrate(x^4*arctanh(c*x^3//2)^2, x) == :(-12//35*c^-10//3*log(1+x*c^2//3+c^1//3*x^(1/2))+-12//35*c^-10//3*log(1+x*c^2//3+-1*c^1//3*x^(1/2))+-1//10*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+-1//10*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//10*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+-1//10*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//10*c^-10//3*Polylogarithms.polylog(2,1/2+(1/2)*c^1//3*x^(1/2))+-1//10*c^-10//3*Polylogarithms.polylog(2,1/2+-1//2*c^1//3*x^(1/2))+1//10*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+1//10*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+1//10*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+1//10*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+1//20*c^-10//3*log(1+-1*c^1//3*x^(1/2))^2+1//20*c^-10//3*log(-1+-1*c^1//3*x^(1/2))^2+1//20*x^5*log(1+c*x^3//2)^2+1//20*x^5*log(1+-1*c*x^3//2)^2+9//70*c^-2*x^2+24//35*c^-10//3*log(1+c^1//3*x^(1/2))+24//35*c^-10//3*log(1+-1*c^1//3*x^(1/2))+-24//35*3^(1/2)*c^-10//3*arctan(1//3*3^(1/2)*(1+-2*c^1//3*x^(1/2)))+-24//35*3^(1/2)*c^-10//3*arctan(1//3*3^(1/2)*(1+2*c^1//3*x^(1/2)))+-3//5*c^-3*x^(1/2)*log(1+-1*c*x^3//2)+-3//35*c^-1*x^7//2*log(1+-1*c*x^3//2)+-1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+-1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+-1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+-1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+-1*c^1//3*x^(1/2))+-1//10*c^-10//3*log((1+(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//10*c^-10//3*log((1+(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+-1//10*c^-10//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+-1//10*c^-10//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//10*c^-10//3*log(1+c*x^3//2)*log(-1+-1*c^1//3*x^(1/2))+-1//10*c^-10//3*log(1+-1*c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+-1//10*c^-10//3*log(1+-1*c^1//3*x^(1/2))*log(1/2+(1/2)*c^1//3*x^(1/2))+-1//10*c^-10//3*log(1/2+-1//2*c^1//3*x^(1/2))*log(-1+-1*c^1//3*x^(1/2))+-1//10*x^5*log(1+c*x^3//2)*log(1+-1*c*x^3//2)+-1//20*(-1)^1//3*c^-10//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))^2+-1//20*(-1)^1//3*c^-10//3*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))^2+1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1+c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1+-1*c^1//3*x^(1/2))+1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+1//10*(-1)^2//3*c^-10//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+1//10*c^-10//3*log((1+(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+1//10*c^-10//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+1//10*c^-10//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+1//10*c^-10//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+1//10*c^-10//3*log(1+c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+1//10*c^-10//3*log(1+-1*c*x^3//2)*log(-1+-1*c^1//3*x^(1/2))+1//20*(-1)^2//3*c^-10//3*log(1+(-1)^1//3*c^1//3*x^(1/2))^2+1//20*(-1)^2//3*c^-10//3*log(-1+(-1)^1//3*c^1//3*x^(1/2))^2+3//5*c^-3*x^(1/2)*log(1+c*x^3//2)+3//35*c^-1*x^7//2*log(1+c*x^3//2)+-1//10*(-1)^1//3*c^-10//3*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//10*(-1)^1//3*c^-10//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//10*(-1)^1//3*c^-10//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//10*(-1)^1//3*c^-10//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//10*(-1)^1//3*c^-10//3*log(1+c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//10*(-1)^1//3*c^-10//3*log(1+-1*c*x^3//2)*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*log(1+c*x^3//2)*log(-1+(-1)^1//3*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*log(1+-1*c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log(1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+-1*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*log(1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+-1//10*(-1)^2//3*c^-10//3*log(-1+(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*log((1+(-1)^1//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//10*(-1)^1//3*c^-10//3*log((1+(-1)^1//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+1//10*(-1)^1//3*c^-10//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*log(1+c*x^3//2)*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*log(1+-1*c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+-1*c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*log(1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//10*(-1)^1//3*c^-10//3*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+c^1//3*x^(1/2))+1//10*(-1)^2//3*c^-10//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+1//10*(-1)^2//3*c^-10//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//10*(-1)^2//3*c^-10//3*log(-1*(-1)^1//3*(1+-1*(-1)^2//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//10*(-1)^2//3*c^-10//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+1//10*(-1)^2//3*c^-10//3*log(1+c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//10*(-1)^2//3*c^-10//3*log(1+-1*c*x^3//2)*log(-1+(-1)^1//3*c^1//3*x^(1/2)))
@test integrate(x*arctanh(c*x^3//2)^2, x) == :(-3//4*c^-4//3*log(1+x*c^2//3+c^1//3*x^(1/2))+-3//4*c^-4//3*log(1+x*c^2//3+-1*c^1//3*x^(1/2))+-1//4*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+-1//4*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//4*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+-1//4*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//4*c^-4//3*Polylogarithms.polylog(2,1/2+(1/2)*c^1//3*x^(1/2))+-1//4*c^-4//3*Polylogarithms.polylog(2,1/2+-1//2*c^1//3*x^(1/2))+1//4*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+1//4*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+1//4*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+1//4*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+1//8*c^-4//3*log(1+-1*c^1//3*x^(1/2))^2+1//8*c^-4//3*log(-1+-1*c^1//3*x^(1/2))^2+1//8*x^2*log(1+c*x^3//2)^2+1//8*x^2*log(1+-1*c*x^3//2)^2+3//2*c^-4//3*log(1+c^1//3*x^(1/2))+3//2*c^-4//3*log(1+-1*c^1//3*x^(1/2))+-3//2*3^(1/2)*c^-4//3*arctan(1//3*3^(1/2)*(1+-2*c^1//3*x^(1/2)))+-3//2*3^(1/2)*c^-4//3*arctan(1//3*3^(1/2)*(1+2*c^1//3*x^(1/2)))+-3//2*c^-1*x^(1/2)*log(1+-1*c*x^3//2)+-1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+-1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+-1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+-1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+-1*c^1//3*x^(1/2))+-1//4*c^-4//3*log((1+(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//4*c^-4//3*log((1+(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+-1//4*c^-4//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+-1//4*c^-4//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//4*c^-4//3*log(1+c*x^3//2)*log(-1+-1*c^1//3*x^(1/2))+-1//4*c^-4//3*log(1+-1*c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+-1//4*c^-4//3*log(1+-1*c^1//3*x^(1/2))*log(1/2+(1/2)*c^1//3*x^(1/2))+-1//4*c^-4//3*log(1/2+-1//2*c^1//3*x^(1/2))*log(-1+-1*c^1//3*x^(1/2))+-1//4*x^2*log(1+c*x^3//2)*log(1+-1*c*x^3//2)+-1//8*(-1)^1//3*c^-4//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))^2+-1//8*(-1)^1//3*c^-4//3*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))^2+1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1+c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1+-1*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+1//4*(-1)^2//3*c^-4//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+1//4*c^-4//3*log((1+(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+1//4*c^-4//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+1//4*c^-4//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+1//4*c^-4//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+1//4*c^-4//3*log(1+c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+1//4*c^-4//3*log(1+-1*c*x^3//2)*log(-1+-1*c^1//3*x^(1/2))+1//8*(-1)^2//3*c^-4//3*log(1+(-1)^1//3*c^1//3*x^(1/2))^2+1//8*(-1)^2//3*c^-4//3*log(-1+(-1)^1//3*c^1//3*x^(1/2))^2+3//2*c^-1*x^(1/2)*log(1+c*x^3//2)+-1//4*(-1)^1//3*c^-4//3*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^-4//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^-4//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^-4//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^-4//3*log(1+c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^1//3*c^-4//3*log(1+-1*c*x^3//2)*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*log(1+c*x^3//2)*log(-1+(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*log(1+-1*c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log(1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+-1*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*log(1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^-4//3*log(-1+(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*log((1+(-1)^1//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^1//3*c^-4//3*log((1+(-1)^1//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+1//4*(-1)^1//3*c^-4//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*log(1+c*x^3//2)*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*log(1+-1*c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+-1*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*log(1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+1//4*(-1)^1//3*c^-4//3*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+c^1//3*x^(1/2))+1//4*(-1)^2//3*c^-4//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^-4//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^-4//3*log(-1*(-1)^1//3*(1+-1*(-1)^2//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^-4//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^-4//3*log(1+c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+1//4*(-1)^2//3*c^-4//3*log(1+-1*c*x^3//2)*log(-1+(-1)^1//3*c^1//3*x^(1/2)))
@test integrate(x^-2*arctanh(c*x^3//2)^2, x) == :((1/2)*c^2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+(1/2)*c^2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+(1/2)*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+(1/2)*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+(1/2)*c^2//3*Polylogarithms.polylog(2,1/2+(1/2)*c^1//3*x^(1/2))+(1/2)*c^2//3*Polylogarithms.polylog(2,1/2+-1//2*c^1//3*x^(1/2))+-1//2*c^2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))+-1//2*c^2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//2*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))+-1//2*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))+-1//4*c^2//3*log(1+-1*c^1//3*x^(1/2))^2+-1//4*c^2//3*log(-1+-1*c^1//3*x^(1/2))^2+-1//4*x^-1*log(1+c*x^3//2)^2+-1//4*x^-1*log(1+-1*c*x^3//2)^2+(1/2)*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+(1/2)*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+(1/2)*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+(1/2)*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+(1/2)*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1+-1*c^1//3*x^(1/2))+(1/2)*c^2//3*log((1+(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+(1/2)*c^2//3*log((1+(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+(1/2)*c^2//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+(1/2)*c^2//3*log(-1*(1+-1*(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+(1/2)*c^2//3*log(1+c*x^3//2)*log(-1+-1*c^1//3*x^(1/2))+(1/2)*c^2//3*log(1+-1*c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+(1/2)*c^2//3*log(1+-1*c^1//3*x^(1/2))*log(1/2+(1/2)*c^1//3*x^(1/2))+(1/2)*c^2//3*log(1/2+-1//2*c^1//3*x^(1/2))*log(-1+-1*c^1//3*x^(1/2))+(1/2)*x^-1*log(1+c*x^3//2)*log(1+-1*c*x^3//2)+-1//2*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,(1+(-1)^2//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1+c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^1//3)^-1+-1*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,(1+(-1)^1//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+(-1)^1//3*c^1//3*x^(1/2)))+-1//2*(-1)^2//3*c^2//3*Polylogarithms.polylog(2,(1+-1*(-1)^2//3)^-1*(1+-1*(-1)^1//3*c^1//3*x^(1/2)))+-1//2*c^2//3*log((1+(-1)^1//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//2*c^2//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+-1//2*c^2//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+c^1//3*x^(1/2)))*log(-1+-1*c^1//3*x^(1/2))+-1//2*c^2//3*log(-1*(1+-1*(-1)^2//3)^-1*((-1)^2//3+-1*c^1//3*x^(1/2)))*log(1+-1*c^1//3*x^(1/2))+-1//2*c^2//3*log(1+c*x^3//2)*log(1+-1*c^1//3*x^(1/2))+-1//2*c^2//3*log(1+-1*c*x^3//2)*log(-1+-1*c^1//3*x^(1/2))+-1//4*(-1)^2//3*c^2//3*log(1+(-1)^1//3*c^1//3*x^(1/2))^2+-1//4*(-1)^2//3*c^2//3*log(-1+(-1)^1//3*c^1//3*x^(1/2))^2+1//4*(-1)^1//3*c^2//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))^2+1//4*(-1)^1//3*c^2//3*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))^2+(1/2)*(-1)^1//3*c^2//3*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^2//3*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^2//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^2//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^2//3*log(1+c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^1//3*c^2//3*log(1+-1*c*x^3//2)*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*log(-1*(-1)^1//3*(1+-1*(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*log(1+c*x^3//2)*log(-1+(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*log(1+-1*c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log(1/2+-1//2*(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*log(1+(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+-1*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*log(1/2+(1/2)*(-1)^1//3*c^1//3*x^(1/2))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+(1/2)*(-1)^2//3*c^2//3*log(-1+(-1)^1//3*c^1//3*x^(1/2))*log((-1)^1//3+c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*log((1+(-1)^1//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+-1*(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^1//3*c^2//3*log((1+(-1)^1//3)^-1*(1+-1*(-1)^2//3*c^1//3*x^(1/2)))*log((1+(-1)^1//3)^-1*((-1)^1//3+(-1)^2//3*c^1//3*x^(1/2)))+-1//2*(-1)^1//3*c^2//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+c^1//3*x^(1/2)))*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*log((-1)^2//3*(1+(-1)^2//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*log(1+c*x^3//2)*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*log(1+-1*c*x^3//2)*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(1/2+(1/2)*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*log(1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+-1*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*log(1/2+-1//2*(-1)^2//3*c^1//3*x^(1/2))*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))+-1//2*(-1)^1//3*c^2//3*log(-1+-1*(-1)^2//3*c^1//3*x^(1/2))*log(-1*(-1)^2//3+c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^2//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+c^1//3*x^(1/2)))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^2//3*log((-1)^1//3*(1+(-1)^1//3)^-1*(1+-1*c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^2//3*log(-1*(-1)^1//3*(1+-1*(-1)^2//3)^-1*((-1)^1//3+c^1//3*x^(1/2)))*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^2//3*log(-1*(-1)^2//3*(1+-1*(-1)^2//3)^-1*(1+(-1)^2//3*c^1//3*x^(1/2)))*log(-1+(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^2//3*log(1+c*x^3//2)*log(1+(-1)^1//3*c^1//3*x^(1/2))+-1//2*(-1)^2//3*c^2//3*log(1+-1*c*x^3//2)*log(-1+(-1)^1//3*c^1//3*x^(1/2)))
@test integrate(x^-1*(a+b*arctanh(c*x^n)), x) == :(a*log(x)+(1/2)*b*n^-1*Polylogarithms.polylog(2,c*x^n)+-1//2*b*n^-1*Polylogarithms.polylog(2,-1*c*x^n))
@test integrate(x^-1*(a+b*arctanh(c*x^n))^2, x) == :((1/2)*b^2*n^-1*Polylogarithms.polylog(3,1+-2*(1+-1*c*x^n)^-1)+2*n^-1*(a+b*arctanh(c*x^n))^2*arctanh(1+-2*(1+-1*c*x^n)^-1)+-1//2*b^2*n^-1*Polylogarithms.polylog(3,-1+2*(1+-1*c*x^n)^-1)+b*n^-1*(a+b*arctanh(c*x^n))*Polylogarithms.polylog(2,-1+2*(1+-1*c*x^n)^-1)+-1*b*n^-1*(a+b*arctanh(c*x^n))*Polylogarithms.polylog(2,1+-2*(1+-1*c*x^n)^-1))
@test integrate(x^-1*arctanh(a*x^n), x) == :((1/2)*n^-1*Polylogarithms.polylog(2,a*x^n)+-1//2*n^-1*Polylogarithms.polylog(2,-1*a*x^n))
@test integrate(x^-1*arctanh(a*x^5), x) == :(-1//10*Polylogarithms.polylog(2,-1*a*x^5)+1//10*Polylogarithms.polylog(2,a*x^5))
@test integrate(arctanh(x^-1), x) == :((1/2)*log(1+-1*x^2)+x*arctanh(x^-1))

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.2 (d x)^m (a+b arctanh(c x^n))^p.jl