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

@test integrate(x^4*exp(arctanh(a*x)), x) == :(3//8*a^-5*arcsin(a*x)+-4//15*a^-3*x^2*(1+-1*a^2*x^2)^(1/2)+-1//4*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)+-1//5*a^-1*x^4*(1+-1*a^2*x^2)^(1/2)+-1//120*a^-5*(1+-1*a^2*x^2)^(1/2)*(64+45*a*x))
@test integrate(x^3*exp(arctanh(a*x)), x) == :(3//8*a^-4*arcsin(a*x)+-1//3*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)+-1//4*a^-1*x^3*(1+-1*a^2*x^2)^(1/2)+-1//24*a^-4*(1+-1*a^2*x^2)^(1/2)*(16+9*a*x))
@test integrate(x^2*exp(arctanh(a*x)), x) == :((1/2)*a^-3*arcsin(a*x)+-1*a^-3*(1+-1*a^2*x^2)^(1/2)+1//3*a^-3*(1+-1*a^2*x^2)^3//2+-1//2*x*a^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x*exp(arctanh(a*x)), x) == :((1/2)*a^-2*arcsin(a*x)+-1//2*a^-2*(1+-1*a^2*x^2)^(1/2)*(2+a*x))
@test integrate(exp(arctanh(a*x)), x) == :(a^-1*arcsin(a*x)+-1*a^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-1*exp(arctanh(a*x)), x) == :(-1*arctanh((1+-1*a^2*x^2)^(1/2))+arcsin(a*x))
@test integrate(x^-2*exp(arctanh(a*x)), x) == :(-1*a*arctanh((1+-1*a^2*x^2)^(1/2))+-1*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-3*exp(arctanh(a*x)), x) == :(-1//2*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)+-1*a*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-4*exp(arctanh(a*x)), x) == :(-1//2*a^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*x^-3*(1+-1*a^2*x^2)^(1/2)+-2//3*a^2*x^-1*(1+-1*a^2*x^2)^(1/2)+-1//2*a*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-5*exp(arctanh(a*x)), x) == :(-3//8*a^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//4*x^-4*(1+-1*a^2*x^2)^(1/2)+-3//8*a^2*x^-2*(1+-1*a^2*x^2)^(1/2)+-2//3*a^3*x^-1*(1+-1*a^2*x^2)^(1/2)+-1//3*a*x^-3*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^3*exp(2*arctanh(a*x)), x) == :(-1//4*x^4+-1*a^-2*x^2+-2*x*a^-3+-2*a^-4*log(1+-1*a*x)+-2//3*a^-1*x^3)
@test integrate(x^2*exp(2*arctanh(a*x)), x) == :(-1//3*x^3+-1*a^-1*x^2+-2*x*a^-2+-2*a^-3*log(1+-1*a*x))
@test integrate(x*exp(2*arctanh(a*x)), x) == :(-1//2*x^2+-2*x*a^-1+-2*a^-2*log(1+-1*a*x))
@test integrate(exp(2*arctanh(a*x)), x) == :(-1x+-2*a^-1*log(1+-1*a*x))
@test integrate(x^-1*exp(2*arctanh(a*x)), x) == :(-2*log(1+-1*a*x)+log(x))
@test integrate(x^-2*exp(2*arctanh(a*x)), x) == :(-1*x^-1+-2*a*log(1+-1*a*x)+2*a*log(x))
@test integrate(x^-3*exp(2*arctanh(a*x)), x) == :(-1//2*x^-2+-2*a*x^-1+-2*a^2*log(1+-1*a*x)+2*a^2*log(x))
@test integrate(x^-4*exp(2*arctanh(a*x)), x) == :(-1//3*x^-3+-1*a*x^-2+-2*a^2*x^-1+-2*a^3*log(1+-1*a*x)+2*a^3*log(x))
@test integrate(x^2*exp(3*arctanh(a*x)), x) == :(-11//2*a^-3*arcsin(a*x)+a^-3*(1+a*x)^3*(1+-1*a^2*x^2)^-1//2+1//3*a^-3*(1+-1*a^2*x^2)^(1/2)*(3+a*x)^2+1//6*a^-3*(1+-1*a^2*x^2)^(1/2)*(28+3*a*x))
@test integrate(x*exp(3*arctanh(a*x)), x) == :(-9//2*a^-2*arcsin(a*x)+9//2*a^-2*(1+-1*a^2*x^2)^(1/2)+a^-2*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^5//2+3//2*a^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^3//2)
@test integrate(exp(3*arctanh(a*x)), x) == :(-3*a^-1*arcsin(a*x)+3*a^-1*(1+-1*a^2*x^2)^(1/2)+2*a^-1*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2)
@test integrate(x^-1*exp(3*arctanh(a*x)), x) == :(-1*arcsin(a*x)+-1*arctanh((1+-1*a^2*x^2)^(1/2))+4*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-2*exp(3*arctanh(a*x)), x) == :(-1*x^-1*(1+-1*a^2*x^2)^(1/2)+-3*a*arctanh((1+-1*a^2*x^2)^(1/2))+4*a*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-3*exp(3*arctanh(a*x)), x) == :(-9//2*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)+-3*a*x^-1*(1+-1*a^2*x^2)^(1/2)+4*a^2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-4*exp(3*arctanh(a*x)), x) == :(-11//2*a^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*x^-3*(1+-1*a^2*x^2)^(1/2)+4*a^3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-14//3*a^2*x^-1*(1+-1*a^2*x^2)^(1/2)+-3//2*a*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^3*exp(4*arctanh(a*x)), x) == :(1//4*x^4+4*a^-4*(1+-1*a*x)^-1+4*a^-2*x^2+12*x*a^-3+16*a^-4*log(1+-1*a*x)+4//3*a^-1*x^3)
@test integrate(x^2*exp(4*arctanh(a*x)), x) == :(1//3*x^3+2*a^-1*x^2+4*a^-3*(1+-1*a*x)^-1+8*x*a^-2+12*a^-3*log(1+-1*a*x))
@test integrate(x*exp(4*arctanh(a*x)), x) == :((1/2)*x^2+4*x*a^-1+4*a^-2*(1+-1*a*x)^-1+8*a^-2*log(1+-1*a*x))
@test integrate(exp(4*arctanh(a*x)), x) == :(x+4*a^-1*(1+-1*a*x)^-1+4*a^-1*log(1+-1*a*x))
@test integrate(x^-1*exp(4*arctanh(a*x)), x) == :(4*(1+-1*a*x)^-1+log(x))
@test integrate(x^-2*exp(4*arctanh(a*x)), x) == :(-1*x^-1+-4*a*log(1+-1*a*x)+4*a*(1+-1*a*x)^-1+4*a*log(x))
@test integrate(x^-3*exp(4*arctanh(a*x)), x) == :(-1//2*x^-2+-8*a^2*log(1+-1*a*x)+-4*a*x^-1+4*a^2*(1+-1*a*x)^-1+8*a^2*log(x))
@test integrate(x^-4*exp(4*arctanh(a*x)), x) == :(-1//3*x^-3+-12*a^3*log(1+-1*a*x)+-8*a^2*x^-1+-2*a*x^-2+4*a^3*(1+-1*a*x)^-1+12*a^3*log(x))
@test integrate(x^3*exp(-1*arctanh(a*x)), x) == :(-3//8*a^-4*arcsin(a*x)+-1//3*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)+-1//24*a^-4*(1+-1*a^2*x^2)^(1/2)*(16+-9*a*x)+1//4*a^-1*x^3*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^2*exp(-1*arctanh(a*x)), x) == :(a^-3*(1+-1*a^2*x^2)^(1/2)+(1/2)*a^-3*arcsin(a*x)+-1//3*a^-3*(1+-1*a^2*x^2)^3//2+-1//2*x*a^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x*exp(-1*arctanh(a*x)), x) == :(-1//2*a^-2*arcsin(a*x)+-1//2*a^-2*(1+-1*a^2*x^2)^(1/2)*(2+-1*a*x))
@test integrate(exp(-1*arctanh(a*x)), x) == :(a^-1*(1+-1*a^2*x^2)^(1/2)+a^-1*arcsin(a*x))
@test integrate(x^-1*exp(-1*arctanh(a*x)), x) == :(-1*arcsin(a*x)+-1*arctanh((1+-1*a^2*x^2)^(1/2)))
@test integrate(x^-2*exp(-1*arctanh(a*x)), x) == :(a*arctanh((1+-1*a^2*x^2)^(1/2))+-1*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-3*exp(-1*arctanh(a*x)), x) == :(-1//2*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)+a*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-4*exp(-1*arctanh(a*x)), x) == :((1/2)*a^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*x^-3*(1+-1*a^2*x^2)^(1/2)+(1/2)*a*x^-2*(1+-1*a^2*x^2)^(1/2)+-2//3*a^2*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-5*exp(-1*arctanh(a*x)), x) == :(-3//8*a^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//4*x^-4*(1+-1*a^2*x^2)^(1/2)+-3//8*a^2*x^-2*(1+-1*a^2*x^2)^(1/2)+1//3*a*x^-3*(1+-1*a^2*x^2)^(1/2)+2//3*a^3*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^3*exp(-2*arctanh(a*x)), x) == :(-1//4*x^4+-1*a^-2*x^2+-2*a^-4*log(1+a*x)+2*x*a^-3+2//3*a^-1*x^3)
@test integrate(x^2*exp(-2*arctanh(a*x)), x) == :(-1//3*x^3+a^-1*x^2+-2*x*a^-2+2*a^-3*log(1+a*x))
@test integrate(x*exp(-2*arctanh(a*x)), x) == :(-1//2*x^2+-2*a^-2*log(1+a*x)+2*x*a^-1)
@test integrate(exp(-2*arctanh(a*x)), x) == :(-1x+2*a^-1*log(1+a*x))
@test integrate(x^-1*exp(-2*arctanh(a*x)), x) == :(-2*log(1+a*x)+log(x))
@test integrate(x^-2*exp(-2*arctanh(a*x)), x) == :(-1*x^-1+-2*a*log(x)+2*a*log(1+a*x))
@test integrate(x^-3*exp(-2*arctanh(a*x)), x) == :(-1//2*x^-2+-2*a^2*log(1+a*x)+2*a*x^-1+2*a^2*log(x))
@test integrate(x^-4*exp(-2*arctanh(a*x)), x) == :(-1//3*x^-3+a*x^-2+-2*a^2*x^-1+-2*a^3*log(x)+2*a^3*log(1+a*x))
@test integrate(x^3*exp(-3*arctanh(a*x)), x) == :(27//4*a^-4*(1+-1*a^2*x^2)^(1/2)+51//8*a^-4*arcsin(a*x)+a^-4*(1+-1*a*x)^3*(1+-1*a^2*x^2)^-1//2+a^-2*x^2*(1+-1*a^2*x^2)^(1/2)+-1//4*a^-1*x^3*(1+-1*a^2*x^2)^(1/2)+1//8*a^-4*(1+-1*a^2*x^2)^(1/2)*(18+-27*a*x))
@test integrate(x^2*exp(-3*arctanh(a*x)), x) == :(-11//2*a^-3*arcsin(a*x)+-1*a^-3*(1+-1*a*x)^3*(1+-1*a^2*x^2)^-1//2+-1//3*a^-3*(1+-1*a^2*x^2)^(1/2)*(3+-1*a*x)^2+-1//6*a^-3*(1+-1*a^2*x^2)^(1/2)*(28+-3*a*x))
@test integrate(x*exp(-3*arctanh(a*x)), x) == :(9//2*a^-2*(1+-1*a^2*x^2)^(1/2)+9//2*a^-2*arcsin(a*x)+a^-2*(1+a*x)^-3*(1+-1*a^2*x^2)^5//2+3//2*a^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^3//2)
@test integrate(exp(-3*arctanh(a*x)), x) == :(-3*a^-1*(1+-1*a^2*x^2)^(1/2)+-3*a^-1*arcsin(a*x)+-2*a^-1*(1+-1*a*x)^2*(1+-1*a^2*x^2)^-1//2)
@test integrate(x^-1*exp(-3*arctanh(a*x)), x) == :(-1*arctanh((1+-1*a^2*x^2)^(1/2))+4*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)+arcsin(a*x))
@test integrate(x^-2*exp(-3*arctanh(a*x)), x) == :(-1*x^-1*(1+-1*a^2*x^2)^(1/2)+3*a*arctanh((1+-1*a^2*x^2)^(1/2))+-4*a*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-3*exp(-3*arctanh(a*x)), x) == :(-9//2*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)+3*a*x^-1*(1+-1*a^2*x^2)^(1/2)+4*a^2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-4*exp(-3*arctanh(a*x)), x) == :(-1//3*x^-3*(1+-1*a^2*x^2)^(1/2)+11//2*a^3*arctanh((1+-1*a^2*x^2)^(1/2))+-4*a^3*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-14//3*a^2*x^-1*(1+-1*a^2*x^2)^(1/2)+3//2*a*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-5*exp(-3*arctanh(a*x)), x) == :(-51//8*a^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//4*x^-4*(1+-1*a^2*x^2)^(1/2)+a*x^-3*(1+-1*a^2*x^2)^(1/2)+4*a^4*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)+6*a^3*x^-1*(1+-1*a^2*x^2)^(1/2)+-19//8*a^2*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^2*exp((1/2)*arctanh(a*x)), x) == :(-3//8*a^-3*(1+a*x)^1//4*(1+-1*a*x)^3//4+-3//16*2^(1/2)*a^-3*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-3//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//12*a^-3*(1+a*x)^5//4*(1+-1*a*x)^3//4+3//16*2^(1/2)*a^-3*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+3//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//3*x*a^-2*(1+a*x)^5//4*(1+-1*a*x)^3//4)
@test integrate(x*exp((1/2)*arctanh(a*x)), x) == :(-1//2*a^-2*(1+a*x)^5//4*(1+-1*a*x)^3//4+-1//4*a^-2*(1+a*x)^1//4*(1+-1*a*x)^3//4+-1//8*2^(1/2)*a^-2*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+1//8*2^(1/2)*a^-2*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+1//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(exp((1/2)*arctanh(a*x)), x) == :((1/2)*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*a^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4+-1//2*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+1//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-1*exp((1/2)*arctanh(a*x)), x) == :(-2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+2^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-2*exp((1/2)*arctanh(a*x)), x) == :(-1*a*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1*a*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1*x^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4)
@test integrate(x^-3*exp((1/2)*arctanh(a*x)), x) == :(-1//4*a^2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//4*a^2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//2*x^-2*(1+a*x)^5//4*(1+-1*a*x)^3//4+-1//4*a*x^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4)
@test integrate(x^-4*exp((1/2)*arctanh(a*x)), x) == :(-3//8*a^3*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-3//8*a^3*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//3*x^-3*(1+a*x)^1//4*(1+-1*a*x)^3//4+-11//24*a^2*x^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4+-5//12*a*x^-2*(1+a*x)^1//4*(1+-1*a*x)^3//4)
@test integrate(x^-5*exp((1/2)*arctanh(a*x)), x) == :(-11//64*a^4*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-11//64*a^4*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//4*x^-4*(1+a*x)^1//4*(1+-1*a*x)^3//4+-83//192*a^3*x^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4+-29//96*a^2*x^-2*(1+a*x)^1//4*(1+-1*a*x)^3//4+-7//24*a*x^-3*(1+a*x)^1//4*(1+-1*a*x)^3//4)
@test integrate(x^-6*exp((1/2)*arctanh(a*x)), x) == :(-31//128*a^5*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-31//128*a^5*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//5*x^-5*(1+a*x)^1//4*(1+-1*a*x)^3//4+-611//1920*a^4*x^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4+-269//960*a^3*x^-2*(1+a*x)^1//4*(1+-1*a*x)^3//4+-11//48*a^2*x^-3*(1+a*x)^1//4*(1+-1*a*x)^3//4+-9//40*a*x^-4*(1+a*x)^1//4*(1+-1*a*x)^3//4)
@test integrate(x^3*exp(3//2*arctanh(a*x)), x) == :(-123//128*2^(1/2)*a^-4*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-123//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-41//64*a^-4*(1+a*x)^3//4*(1+-1*a*x)^1//4+123//128*2^(1/2)*a^-4*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+123//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//4*a^-2*x^2*(1+a*x)^7//4*(1+-1*a*x)^1//4+-1//32*a^-4*(1+a*x)^7//4*(1+-1*a*x)^1//4*(11+4*a*x))
@test integrate(x^2*exp(3//2*arctanh(a*x)), x) == :(-17//16*2^(1/2)*a^-3*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-17//24*a^-3*(1+a*x)^3//4*(1+-1*a*x)^1//4+-17//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//4*a^-3*(1+a*x)^7//4*(1+-1*a*x)^1//4+17//16*2^(1/2)*a^-3*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+17//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//3*x*a^-2*(1+a*x)^7//4*(1+-1*a*x)^1//4)
@test integrate(x*exp(3//2*arctanh(a*x)), x) == :(-9//8*2^(1/2)*a^-2*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-9//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-3//4*a^-2*(1+a*x)^3//4*(1+-1*a*x)^1//4+-1//2*a^-2*(1+a*x)^7//4*(1+-1*a*x)^1//4+9//8*2^(1/2)*a^-2*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+9//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(exp(3//2*arctanh(a*x)), x) == :(-1*a^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4+-3//2*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-3//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+3//2*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+3//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-1*exp(3//2*arctanh(a*x)), x) == :(-2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+2^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-2*exp(3//2*arctanh(a*x)), x) == :(-3*a*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+3*a*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1*x^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4)
@test integrate(x^-3*exp(3//2*arctanh(a*x)), x) == :(-9//4*a^2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+9//4*a^2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//2*x^-2*(1+a*x)^7//4*(1+-1*a*x)^1//4+-3//4*a*x^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4)
@test integrate(x^-4*exp(3//2*arctanh(a*x)), x) == :(-17//8*a^3*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+17//8*a^3*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//3*x^-3*(1+a*x)^3//4*(1+-1*a*x)^1//4+-23//24*a^2*x^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4+-7//12*a*x^-2*(1+a*x)^3//4*(1+-1*a*x)^1//4)
@test integrate(x^-5*exp(3//2*arctanh(a*x)), x) == :(-123//64*a^4*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+123//64*a^4*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//4*x^-4*(1+a*x)^3//4*(1+-1*a*x)^1//4+-63//64*a^3*x^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4+-15//32*a^2*x^-2*(1+a*x)^3//4*(1+-1*a*x)^1//4+-3//8*a*x^-3*(1+a*x)^3//4*(1+-1*a*x)^1//4)
@test integrate(x^3*exp(5//2*arctanh(a*x)), x) == :(-475//128*2^(1/2)*a^-4*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-475//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+475//64*a^-4*(1+a*x)^1//4*(1+-1*a*x)^3//4+475//128*2^(1/2)*a^-4*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+475//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+4*a^-1*x^3*(1+a*x)^5//4*(1+-1*a*x)^-1//4+1//96*a^-4*(1+a*x)^5//4*(1+-1*a*x)^3//4*(521+452*a*x)+17//4*a^-2*x^2*(1+a*x)^5//4*(1+-1*a*x)^3//4)
@test integrate(x^2*exp(5//2*arctanh(a*x)), x) == :(2*a^-3*(1+a*x)^9//4*(1+-1*a*x)^-1//4+-55//16*2^(1/2)*a^-3*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-55//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+1//3*a^-3*(1+a*x)^9//4*(1+-1*a*x)^3//4+11//4*a^-3*(1+a*x)^5//4*(1+-1*a*x)^3//4+55//8*a^-3*(1+a*x)^1//4*(1+-1*a*x)^3//4+55//16*2^(1/2)*a^-3*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+55//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x*exp(5//2*arctanh(a*x)), x) == :(2*a^-2*(1+a*x)^9//4*(1+-1*a*x)^-1//4+-25//8*2^(1/2)*a^-2*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-25//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+5//2*a^-2*(1+a*x)^5//4*(1+-1*a*x)^3//4+25//4*a^-2*(1+a*x)^1//4*(1+-1*a*x)^3//4+25//8*2^(1/2)*a^-2*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+25//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(exp(5//2*arctanh(a*x)), x) == :(4*a^-1*(1+a*x)^5//4*(1+-1*a*x)^-1//4+5*a^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4+-5//2*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-5//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+5//2*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+5//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-1*exp(5//2*arctanh(a*x)), x) == :(-2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+2^(1/2)*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+8*(1+a*x)^1//4*(1+-1*a*x)^-1//4+-1//2*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-2*exp(5//2*arctanh(a*x)), x) == :(-5*a*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-5*a*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1*x^-1*(1+a*x)^5//4*(1+-1*a*x)^-1//4+10*a*(1+a*x)^1//4*(1+-1*a*x)^-1//4)
@test integrate(x^-3*exp(5//2*arctanh(a*x)), x) == :(-25//4*a^2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-25//4*a^2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//2*x^-2*(1+a*x)^9//4*(1+-1*a*x)^-1//4+25//2*a^2*(1+a*x)^1//4*(1+-1*a*x)^-1//4+-5//4*a*x^-1*(1+a*x)^5//4*(1+-1*a*x)^-1//4)
@test integrate(x^-4*exp(5//2*arctanh(a*x)), x) == :(-55//8*a^3*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-55//8*a^3*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//3*x^-3*(1+a*x)^1//4*(1+-1*a*x)^-1//4+287//24*a^3*(1+a*x)^1//4*(1+-1*a*x)^-1//4+-61//24*a^2*x^-1*(1+a*x)^1//4*(1+-1*a*x)^-1//4+-13//12*a*x^-2*(1+a*x)^1//4*(1+-1*a*x)^-1//4)
@test integrate(x^-5*exp(5//2*arctanh(a*x)), x) == :(-475//64*a^4*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-475//64*a^4*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//4*x^-4*(1+a*x)^1//4*(1+-1*a*x)^-1//4+2467//192*a^4*(1+a*x)^1//4*(1+-1*a*x)^-1//4+-521//192*a^3*x^-1*(1+a*x)^1//4*(1+-1*a*x)^-1//4+-113//96*a^2*x^-2*(1+a*x)^1//4*(1+-1*a*x)^-1//4+-17//24*a*x^-3*(1+a*x)^1//4*(1+-1*a*x)^-1//4)
@test integrate(x^3*exp(-1//2*arctanh(a*x)), x) == :(-11//64*a^-4*(1+a*x)^3//4*(1+-1*a*x)^1//4+-11//128*2^(1/2)*a^-4*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-11//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+11//128*2^(1/2)*a^-4*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+11//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//4*a^-2*x^2*(1+a*x)^3//4*(1+-1*a*x)^5//4+-1//96*a^-4*(1+a*x)^3//4*(1+-1*a*x)^5//4*(25+-4*a*x))
@test integrate(x^2*exp(-1//2*arctanh(a*x)), x) == :(-3//16*2^(1/2)*a^-3*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-3//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+1//12*a^-3*(1+a*x)^3//4*(1+-1*a*x)^5//4+3//8*a^-3*(1+a*x)^3//4*(1+-1*a*x)^1//4+3//16*2^(1/2)*a^-3*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+3//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//3*x*a^-2*(1+a*x)^3//4*(1+-1*a*x)^5//4)
@test integrate(x*exp(-1//2*arctanh(a*x)), x) == :(-1//2*a^-2*(1+a*x)^3//4*(1+-1*a*x)^5//4+-1//4*a^-2*(1+a*x)^3//4*(1+-1*a*x)^1//4+-1//8*2^(1/2)*a^-2*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+1//8*2^(1/2)*a^-2*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+1//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(exp(-1//2*arctanh(a*x)), x) == :(a^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4+(1/2)*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+1//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-1*exp(-1//2*arctanh(a*x)), x) == :(-2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+2^(1/2)*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-2*exp(-1//2*arctanh(a*x)), x) == :(a*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1*a*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1*x^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4)
@test integrate(x^-3*exp(-1//2*arctanh(a*x)), x) == :(-1//4*a^2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+1//4*a^2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//2*x^-2*(1+a*x)^3//4*(1+-1*a*x)^5//4+1//4*a*x^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4)
@test integrate(x^-4*exp(-1//2*arctanh(a*x)), x) == :(-3//8*a^3*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+3//8*a^3*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//3*x^-3*(1+a*x)^3//4*(1+-1*a*x)^1//4+-11//24*a^2*x^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4+5//12*a*x^-2*(1+a*x)^3//4*(1+-1*a*x)^1//4)
@test integrate(x^-5*exp(-1//2*arctanh(a*x)), x) == :(-11//64*a^4*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+11//64*a^4*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//4*x^-4*(1+a*x)^3//4*(1+-1*a*x)^1//4+-29//96*a^2*x^-2*(1+a*x)^3//4*(1+-1*a*x)^1//4+7//24*a*x^-3*(1+a*x)^3//4*(1+-1*a*x)^1//4+83//192*a^3*x^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4)
@test integrate(x^3*exp(-3//2*arctanh(a*x)), x) == :(-123//128*2^(1/2)*a^-4*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-123//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-41//64*a^-4*(1+a*x)^1//4*(1+-1*a*x)^3//4+123//128*2^(1/2)*a^-4*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+123//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//4*a^-2*x^2*(1+a*x)^1//4*(1+-1*a*x)^7//4+-1//32*a^-4*(1+a*x)^1//4*(1+-1*a*x)^7//4*(11+-4*a*x))
@test integrate(x^2*exp(-3//2*arctanh(a*x)), x) == :(-17//16*2^(1/2)*a^-3*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-17//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+1//4*a^-3*(1+a*x)^1//4*(1+-1*a*x)^7//4+17//16*2^(1/2)*a^-3*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+17//24*a^-3*(1+a*x)^1//4*(1+-1*a*x)^3//4+17//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//3*x*a^-2*(1+a*x)^1//4*(1+-1*a*x)^7//4)
@test integrate(x*exp(-3//2*arctanh(a*x)), x) == :(-9//8*2^(1/2)*a^-2*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-9//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-3//4*a^-2*(1+a*x)^1//4*(1+-1*a*x)^3//4+-1//2*a^-2*(1+a*x)^1//4*(1+-1*a*x)^7//4+9//8*2^(1/2)*a^-2*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+9//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(exp(-3//2*arctanh(a*x)), x) == :(a^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4+-3//2*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-3//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+3//2*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+3//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-1*exp(-3//2*arctanh(a*x)), x) == :(-2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+2^(1/2)*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-2*exp(-3//2*arctanh(a*x)), x) == :(3*a*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+3*a*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1*x^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4)
@test integrate(x^-3*exp(-3//2*arctanh(a*x)), x) == :(-9//4*a^2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-9//4*a^2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//2*x^-2*(1+a*x)^1//4*(1+-1*a*x)^7//4+3//4*a*x^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4)
@test integrate(x^-4*exp(-3//2*arctanh(a*x)), x) == :(17//8*a^3*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+17//8*a^3*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//3*x^-3*(1+a*x)^1//4*(1+-1*a*x)^3//4+-23//24*a^2*x^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4+7//12*a*x^-2*(1+a*x)^1//4*(1+-1*a*x)^3//4)
@test integrate(x^-5*exp(-3//2*arctanh(a*x)), x) == :(-123//64*a^4*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-123//64*a^4*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//4*x^-4*(1+a*x)^1//4*(1+-1*a*x)^3//4+-15//32*a^2*x^-2*(1+a*x)^1//4*(1+-1*a*x)^3//4+3//8*a*x^-3*(1+a*x)^1//4*(1+-1*a*x)^3//4+63//64*a^3*x^-1*(1+a*x)^1//4*(1+-1*a*x)^3//4)
@test integrate(x^3*exp(-5//2*arctanh(a*x)), x) == :(-475//128*2^(1/2)*a^-4*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-475//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+475//64*a^-4*(1+a*x)^3//4*(1+-1*a*x)^1//4+475//128*2^(1/2)*a^-4*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+475//256*2^(1/2)*a^-4*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-4*a^-1*x^3*(1+a*x)^-1//4*(1+-1*a*x)^5//4+1//96*a^-4*(1+a*x)^3//4*(1+-1*a*x)^5//4*(521+-452*a*x)+17//4*a^-2*x^2*(1+a*x)^3//4*(1+-1*a*x)^5//4)
@test integrate(x^2*exp(-5//2*arctanh(a*x)), x) == :(-2*a^-3*(1+a*x)^-1//4*(1+-1*a*x)^9//4+-55//8*a^-3*(1+a*x)^3//4*(1+-1*a*x)^1//4+-55//16*2^(1/2)*a^-3*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-55//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-11//4*a^-3*(1+a*x)^3//4*(1+-1*a*x)^5//4+-1//3*a^-3*(1+a*x)^3//4*(1+-1*a*x)^9//4+55//16*2^(1/2)*a^-3*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+55//32*2^(1/2)*a^-3*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x*exp(-5//2*arctanh(a*x)), x) == :(2*a^-2*(1+a*x)^-1//4*(1+-1*a*x)^9//4+-25//8*2^(1/2)*a^-2*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-25//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+5//2*a^-2*(1+a*x)^3//4*(1+-1*a*x)^5//4+25//4*a^-2*(1+a*x)^3//4*(1+-1*a*x)^1//4+25//8*2^(1/2)*a^-2*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+25//16*2^(1/2)*a^-2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(exp(-5//2*arctanh(a*x)), x) == :(-5*a^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4+-4*a^-1*(1+a*x)^-1//4*(1+-1*a*x)^5//4+-5//2*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-5//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+5//2*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+5//4*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-1*exp(-5//2*arctanh(a*x)), x) == :(-2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+2^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+8*(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1//2*2^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate(x^-2*exp(-5//2*arctanh(a*x)), x) == :(-5*a*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+5*a*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1*x^-1*(1+a*x)^-1//4*(1+-1*a*x)^5//4+-10*a*(1+a*x)^-1//4*(1+-1*a*x)^1//4)
@test integrate(x^-3*exp(-5//2*arctanh(a*x)), x) == :(-25//4*a^2*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+25//4*a^2*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//2*x^-2*(1+a*x)^-1//4*(1+-1*a*x)^9//4+25//2*a^2*(1+a*x)^-1//4*(1+-1*a*x)^1//4+5//4*a*x^-1*(1+a*x)^-1//4*(1+-1*a*x)^5//4)
@test integrate(x^-4*exp(-5//2*arctanh(a*x)), x) == :(-55//8*a^3*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+55//8*a^3*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-287//24*a^3*(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1//3*x^-3*(1+a*x)^-1//4*(1+-1*a*x)^1//4+-61//24*a^2*x^-1*(1+a*x)^-1//4*(1+-1*a*x)^1//4+13//12*a*x^-2*(1+a*x)^-1//4*(1+-1*a*x)^1//4)
@test integrate(x^-5*exp(-5//2*arctanh(a*x)), x) == :(-475//64*a^4*arctanh((1+a*x)^1//4*(1+-1*a*x)^-1//4)+475//64*a^4*arctan((1+a*x)^1//4*(1+-1*a*x)^-1//4)+-1//4*x^-4*(1+a*x)^-1//4*(1+-1*a*x)^1//4+2467//192*a^4*(1+a*x)^-1//4*(1+-1*a*x)^1//4+-113//96*a^2*x^-2*(1+a*x)^-1//4*(1+-1*a*x)^1//4+17//24*a*x^-3*(1+a*x)^-1//4*(1+-1*a*x)^1//4+521//192*a^3*x^-1*(1+a*x)^-1//4*(1+-1*a*x)^1//4)
@test integrate(x^2*exp(1//3*arctanh(x)), x) == :(-19//81*arctan((1+x)^-1//6*(1+-1x)^1//6)+-19//162*arctan(3^(1/2)+2*(1+x)^-1//6*(1+-1x)^1//6)+19//162*arctan(3^(1/2)+-2*(1+x)^-1//6*(1+-1x)^1//6)+-19//54*(1+x)^1//6*(1+-1x)^5//6+-19//324*3^(1/2)*log(1+(1+x)^-1//3*(1+-1x)^1//3+-1*3^(1/2)*(1+x)^-1//6*(1+-1x)^1//6)+-1//18*(1+x)^7//6*(1+-1x)^5//6+19//324*3^(1/2)*log(1+(1+x)^-1//3*(1+-1x)^1//3+3^(1/2)*(1+x)^-1//6*(1+-1x)^1//6)+-1//3*x*(1+x)^7//6*(1+-1x)^5//6)
@test integrate(x*exp(1//3*arctanh(x)), x) == :(-1//9*arctan((1+x)^-1//6*(1+-1x)^1//6)+-1//18*arctan(3^(1/2)+2*(1+x)^-1//6*(1+-1x)^1//6)+1//18*arctan(3^(1/2)+-2*(1+x)^-1//6*(1+-1x)^1//6)+-1//2*(1+x)^7//6*(1+-1x)^5//6+-1//6*(1+x)^1//6*(1+-1x)^5//6+-1//36*3^(1/2)*log(1+(1+x)^-1//3*(1+-1x)^1//3+-1*3^(1/2)*(1+x)^-1//6*(1+-1x)^1//6)+1//36*3^(1/2)*log(1+(1+x)^-1//3*(1+-1x)^1//3+3^(1/2)*(1+x)^-1//6*(1+-1x)^1//6))
@test integrate(exp(1//3*arctanh(x)), x) == :(-2//3*arctan((1+x)^-1//6*(1+-1x)^1//6)+-1//3*arctan(3^(1/2)+2*(1+x)^-1//6*(1+-1x)^1//6)+1//3*arctan(3^(1/2)+-2*(1+x)^-1//6*(1+-1x)^1//6)+-1*(1+x)^1//6*(1+-1x)^5//6+-1//6*3^(1/2)*log(1+(1+x)^-1//3*(1+-1x)^1//3+-1*3^(1/2)*(1+x)^-1//6*(1+-1x)^1//6)+1//6*3^(1/2)*log(1+(1+x)^-1//3*(1+-1x)^1//3+3^(1/2)*(1+x)^-1//6*(1+-1x)^1//6))
@test integrate(x^-1*exp(1//3*arctanh(x)), x) == :((1/2)*log(1+(1+x)^1//3*(1+-1x)^-1//3+-1*(1+x)^1//6*(1+-1x)^-1//6)+-1*arctan(3^(1/2)+2*(1+x)^-1//6*(1+-1x)^1//6)+-2*arctan((1+x)^-1//6*(1+-1x)^1//6)+-2*arctanh((1+x)^1//6*(1+-1x)^-1//6)+-1//2*log(1+(1+x)^1//3*(1+-1x)^-1//3+(1+x)^1//6*(1+-1x)^-1//6)+3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*(1+x)^1//6*(1+-1x)^-1//6))+(1/2)*3^(1/2)*log(1+(1+x)^-1//3*(1+-1x)^1//3+3^(1/2)*(1+x)^-1//6*(1+-1x)^1//6)+-1*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+x)^1//6*(1+-1x)^-1//6))+-1//2*3^(1/2)*log(1+(1+x)^-1//3*(1+-1x)^1//3+-1*3^(1/2)*(1+x)^-1//6*(1+-1x)^1//6)+arctan(3^(1/2)+-2*(1+x)^-1//6*(1+-1x)^1//6))
@test integrate(x^-2*exp(1//3*arctanh(x)), x) == :(-2//3*arctanh((1+x)^1//6*(1+-1x)^-1//6)+-1//6*log(1+(1+x)^1//3*(1+-1x)^-1//3+(1+x)^1//6*(1+-1x)^-1//6)+1//6*log(1+(1+x)^1//3*(1+-1x)^-1//3+-1*(1+x)^1//6*(1+-1x)^-1//6)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+x)^1//6*(1+-1x)^-1//6))+1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*(1+x)^1//6*(1+-1x)^-1//6))+-1*x^-1*(1+x)^1//6*(1+-1x)^5//6)
@test integrate(x^-3*exp(1//3*arctanh(x)), x) == :(-1//9*arctanh((1+x)^1//6*(1+-1x)^-1//6)+-1//36*log(1+(1+x)^1//3*(1+-1x)^-1//3+(1+x)^1//6*(1+-1x)^-1//6)+1//36*log(1+(1+x)^1//3*(1+-1x)^-1//3+-1*(1+x)^1//6*(1+-1x)^-1//6)+-1//18*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(1+x)^1//6*(1+-1x)^-1//6))+1//18*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*(1+x)^1//6*(1+-1x)^-1//6))+-1//2*x^-2*(1+x)^7//6*(1+-1x)^5//6+-1//6*x^-1*(1+x)^1//6*(1+-1x)^5//6)
@test integrate(x^2*exp(2//3*arctanh(x)), x) == :(11//27*log(1+(1+x)^-1//3*(1+-1x)^1//3)+11//81*log(1+x)+-11//27*(1+x)^1//3*(1+-1x)^2//3+-1//9*(1+x)^4//3*(1+-1x)^2//3+22//81*3^(1/2)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*(1+x)^-1//3*(1+-1x)^1//3)+-1//3*x*(1+x)^4//3*(1+-1x)^2//3)
@test integrate(x*exp(2//3*arctanh(x)), x) == :(1//3*log(1+(1+x)^-1//3*(1+-1x)^1//3)+1//9*log(1+x)+-1//2*(1+x)^4//3*(1+-1x)^2//3+-1//3*(1+x)^1//3*(1+-1x)^2//3+2//9*3^(1/2)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*(1+x)^-1//3*(1+-1x)^1//3))
@test integrate(exp(2//3*arctanh(x)), x) == :(1//3*log(1+x)+-1*(1+x)^1//3*(1+-1x)^2//3+2//3*3^(1/2)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*(1+x)^-1//3*(1+-1x)^1//3)+log(1+(1+x)^-1//3*(1+-1x)^1//3))
@test integrate(x^-1*exp(2//3*arctanh(x)), x) == :((1/2)*log(1+x)+-1//2*log(x)+3//2*log(1+(1+x)^-1//3*(1+-1x)^1//3)+3//2*log((1+-1x)^1//3+-1*(1+x)^1//3)+3^(1/2)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*(1+x)^-1//3*(1+-1x)^1//3)+3^(1/2)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(1+x)^-1//3*(1+-1x)^1//3))
@test integrate(x^-2*exp(2//3*arctanh(x)), x) == :(-1//3*log(x)+2//3*3^(1/2)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(1+x)^-1//3*(1+-1x)^1//3)+-1*x^-1*(1+x)^1//3*(1+-1x)^2//3+log((1+-1x)^1//3+-1*(1+x)^1//3))
@test integrate(x^-3*exp(2//3*arctanh(x)), x) == :(-1//9*log(x)+1//3*log((1+-1x)^1//3+-1*(1+x)^1//3)+2//9*3^(1/2)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(1+x)^-1//3*(1+-1x)^1//3)+-1//2*x^-2*(1+x)^4//3*(1+-1x)^2//3+-1//3*x^-1*(1+x)^1//3*(1+-1x)^2//3)
@test integrate(x^2*exp(1//4*arctanh(a*x)), x) == :(-11//32*a^-3*(1+a*x)^1//8*(1+-1*a*x)^7//8+-11//128*a^-3*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+-11//128*a^-3*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+-11//256*a^-3*(2+2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1*(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+2^(1/2))^(1/2))+-11//256*a^-3*(2+-1*2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1*(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+-1*2^(1/2))^(1/2))+-1//24*a^-3*(1+a*x)^9//8*(1+-1*a*x)^7//8+11//128*a^-3*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+11//128*a^-3*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+11//256*a^-3*(2+2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+2^(1/2))^(1/2))+11//256*a^-3*(2+-1*2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+-1*2^(1/2))^(1/2))+-1//3*x*a^-2*(1+a*x)^9//8*(1+-1*a*x)^7//8)
@test integrate(x*exp(1//4*arctanh(a*x)), x) == :(-1//2*a^-2*(1+a*x)^9//8*(1+-1*a*x)^7//8+-1//8*a^-2*(1+a*x)^1//8*(1+-1*a*x)^7//8+-1//32*a^-2*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+-1//32*a^-2*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+-1//64*a^-2*(2+2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1*(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+2^(1/2))^(1/2))+-1//64*a^-2*(2+-1*2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1*(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+-1*2^(1/2))^(1/2))+1//32*a^-2*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+1//32*a^-2*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+1//64*a^-2*(2+2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+2^(1/2))^(1/2))+1//64*a^-2*(2+-1*2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+-1*2^(1/2))^(1/2)))
@test integrate(exp(1//4*arctanh(a*x)), x) == :(-1*a^-1*(1+a*x)^1//8*(1+-1*a*x)^7//8+-1//4*a^-1*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+-1//4*a^-1*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+-1//8*a^-1*(2+2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1*(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+2^(1/2))^(1/2))+-1//8*a^-1*(2+-1*2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1*(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+-1*2^(1/2))^(1/2))+1//4*a^-1*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+1//4*a^-1*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+1//8*a^-1*(2+2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+2^(1/2))^(1/2))+1//8*a^-1*(2+-1*2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+-1*2^(1/2))^(1/2)))
@test integrate(x^-1*exp(1//4*arctanh(a*x)), x) == :(-2*arctan((1+a*x)^1//8*(1+-1*a*x)^-1//8)+-2*arctanh((1+a*x)^1//8*(1+-1*a*x)^-1//8)+2^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+(1/2)*2^(1/2)*log(1+(1+a*x)^1//4*(1+-1*a*x)^-1//4+-1*2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+(1/2)*(2+2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+2^(1/2))^(1/2))+(1/2)*(2+-1*2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+-1*2^(1/2))^(1/2))+-1*2^(1/2)*arctan(1+2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+-1*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+-1*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2*(1+a*x)^-1//8*(1+-1*a*x)^1//8))+-1//2*2^(1/2)*log(1+(1+a*x)^1//4*(1+-1*a*x)^-1//4+2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+-1//2*(2+2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1*(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+2^(1/2))^(1/2))+-1//2*(2+-1*2^(1/2))^(1/2)*log(1+(1+a*x)^-1//4*(1+-1*a*x)^1//4+-1*(1+a*x)^-1//8*(1+-1*a*x)^1//8*(2+-1*2^(1/2))^(1/2)))
@test integrate(x^-2*exp(1//4*arctanh(a*x)), x) == :(-1//2*a*arctan((1+a*x)^1//8*(1+-1*a*x)^-1//8)+-1//2*a*arctanh((1+a*x)^1//8*(1+-1*a*x)^-1//8)+-1*x^-1*(1+a*x)^1//8*(1+-1*a*x)^7//8+-1//4*a*2^(1/2)*arctan(1+2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+-1//8*a*2^(1/2)*log(1+(1+a*x)^1//4*(1+-1*a*x)^-1//4+2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+1//4*a*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+1//8*a*2^(1/2)*log(1+(1+a*x)^1//4*(1+-1*a*x)^-1//4+-1*2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8))
@test integrate(x^-3*exp(1//4*arctanh(a*x)), x) == :(-1//16*a^2*arctan((1+a*x)^1//8*(1+-1*a*x)^-1//8)+-1//16*a^2*arctanh((1+a*x)^1//8*(1+-1*a*x)^-1//8)+-1//2*x^-2*(1+a*x)^9//8*(1+-1*a*x)^7//8+-1//32*2^(1/2)*a^2*arctan(1+2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+-1//64*2^(1/2)*a^2*log(1+(1+a*x)^1//4*(1+-1*a*x)^-1//4+2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+1//32*2^(1/2)*a^2*arctan(1+-1*2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+1//64*2^(1/2)*a^2*log(1+(1+a*x)^1//4*(1+-1*a*x)^-1//4+-1*2^(1/2)*(1+a*x)^1//8*(1+-1*a*x)^-1//8)+-1//8*a*x^-1*(1+a*x)^1//8*(1+-1*a*x)^7//8)
@test integrate((c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(7//8*x*c^4*(1+-1*a^2*x^2)^(1/2)+7//8*a^-1*c^4*arcsin(a*x)+7//12*a^-1*c^4*(1+-1*a^2*x^2)^3//2+1//5*a^-1*c^4*(1+-1*a*x)^2*(1+-1*a^2*x^2)^3//2+7//20*a^-1*c^4*(1+-1*a^2*x^2)^3//2*(1+-1*a*x))
@test integrate((c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(5//8*x*c^3*(1+-1*a^2*x^2)^(1/2)+5//8*a^-1*c^3*arcsin(a*x)+5//12*a^-1*c^3*(1+-1*a^2*x^2)^3//2+1//4*a^-1*c^3*(1+-1*a^2*x^2)^3//2*(1+-1*a*x))
@test integrate((c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :((1/2)*x*c^2*(1+-1*a^2*x^2)^(1/2)+(1/2)*a^-1*c^2*arcsin(a*x)+1//3*a^-1*c^2*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)*exp(arctanh(a*x)), x) == :((1/2)*c*x*(1+-1*a^2*x^2)^(1/2)+(1/2)*c*a^-1*arcsin(a*x))
@test integrate((c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-1*a^-1*c^-1*arcsin(a*x)+2*a^-1*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(1//3*a^-1*c^-2*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(1//5*a^-1*c^-3*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+1//15*a^-1*c^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(1//7*a^-1*c^-4*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^3//2+2//35*a^-1*c^-4*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+2//105*a^-1*c^-4*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^-5*exp(arctanh(a*x)), x) == :(1//9*a^-1*c^-5*(1+-1*a*x)^-6*(1+-1*a^2*x^2)^3//2+1//21*a^-1*c^-5*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^3//2+2//105*a^-1*c^-5*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+2//315*a^-1*c^-5*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^p*exp(2*arctanh(a*x)), x) == :(-2*a^-1*p^-1*(c+-1*a*c*x)^p+a^-1*c^-1*(1+p)^-1*(c+-1*a*c*x)^(1+p))
@test integrate((c+-1*a*c*x)^5*exp(2*arctanh(a*x)), x) == :(-2//5*a^-1*c^5*(1+-1*a*x)^5+1//6*a^-1*c^5*(1+-1*a*x)^6)
@test integrate((c+-1*a*c*x)^4*exp(2*arctanh(a*x)), x) == :(-1//2*a^-1*c^4*(1+-1*a*x)^4+1//5*a^-1*c^4*(1+-1*a*x)^5)
@test integrate((c+-1*a*c*x)^3*exp(2*arctanh(a*x)), x) == :(-2//3*a^-1*c^3*(1+-1*a*x)^3+1//4*a^-1*c^3*(1+-1*a*x)^4)
@test integrate((c+-1*a*c*x)^2*exp(2*arctanh(a*x)), x) == :(x*c^2+-1//3*a^2*c^2*x^3)
@test integrate((c+-1*a*c*x)^-1*exp(2*arctanh(a*x)), x) == :(a^-1*c^-1*log(1+-1*a*x)+2*a^-1*c^-1*(1+-1*a*x)^-1)
@test integrate((c+-1*a*c*x)^-2*exp(2*arctanh(a*x)), x) == :(x*c^-2*(1+-1*a*x)^-2)
@test integrate((c+-1*a*c*x)^-3*exp(2*arctanh(a*x)), x) == :(-1//2*a^-1*c^-3*(1+-1*a*x)^-2+2//3*a^-1*c^-3*(1+-1*a*x)^-3)
@test integrate((c+-1*a*c*x)^-4*exp(2*arctanh(a*x)), x) == :((1/2)*a^-1*c^-4*(1+-1*a*x)^-4+-1//3*a^-1*c^-4*(1+-1*a*x)^-3)
@test integrate((c+-1*a*c*x)^4*exp(3*arctanh(a*x)), x) == :(1//4*x*c^4*(1+-1*a^2*x^2)^3//2+1//5*a^-1*c^4*(1+-1*a^2*x^2)^5//2+3//8*x*c^4*(1+-1*a^2*x^2)^(1/2)+3//8*a^-1*c^4*arcsin(a*x))
@test integrate((c+-1*a*c*x)^3*exp(3*arctanh(a*x)), x) == :(1//4*x*c^3*(1+-1*a^2*x^2)^3//2+3//8*x*c^3*(1+-1*a^2*x^2)^(1/2)+3//8*a^-1*c^3*arcsin(a*x))
@test integrate((c+-1*a*c*x)^2*exp(3*arctanh(a*x)), x) == :((1/2)*x*c^2*(1+-1*a^2*x^2)^(1/2)+(1/2)*a^-1*c^2*arcsin(a*x)+-1//3*a^-1*c^2*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)*exp(3*arctanh(a*x)), x) == :(-3//2*c*a^-1*(1+-1*a^2*x^2)^(1/2)+3//2*c*a^-1*arcsin(a*x)+-1//2*c*a^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^-1*exp(3*arctanh(a*x)), x) == :(a^-1*c^-1*arcsin(a*x)+-2*a^-1*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+2//3*a^-1*c^-1*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^-2*exp(3*arctanh(a*x)), x) == :(1//5*a^-1*c^-2*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^5//2)
@test integrate((c+-1*a*c*x)^-3*exp(3*arctanh(a*x)), x) == :(1//7*a^-1*c^-3*(1+-1*a*x)^-6*(1+-1*a^2*x^2)^5//2+1//35*a^-1*c^-3*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^5//2)
@test integrate((c+-1*a*c*x)^-4*exp(3*arctanh(a*x)), x) == :(1//9*a^-1*c^-4*(1+-1*a*x)^-7*(1+-1*a^2*x^2)^5//2+2//63*a^-1*c^-4*(1+-1*a*x)^-6*(1+-1*a^2*x^2)^5//2+2//315*a^-1*c^-4*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^5//2)
@test integrate((c+-1*a*c*x)^-5*exp(3*arctanh(a*x)), x) == :(1//11*a^-1*c^-5*(1+-1*a*x)^-8*(1+-1*a^2*x^2)^5//2+1//33*a^-1*c^-5*(1+-1*a*x)^-7*(1+-1*a^2*x^2)^5//2+2//231*a^-1*c^-5*(1+-1*a*x)^-6*(1+-1*a^2*x^2)^5//2+2//1155*a^-1*c^-5*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^5//2)
@test integrate((c+-1*a*c*x)^p*exp(4*arctanh(a*x)), x) == :(4*a^-1*p^-1*(c+-1*a*c*x)^p+-1*a^-1*c^-1*(1+p)^-1*(c+-1*a*c*x)^(1+p)+4*c*a^-1*(1+-1p)^-1*(c+-1*a*c*x)^(-1+p))
@test integrate((c+-1*a*c*x)^5*exp(4*arctanh(a*x)), x) == :(-1*a^-1*c^5*(1+-1*a*x)^4+-1//6*a^-1*c^5*(1+-1*a*x)^6+4//5*a^-1*c^5*(1+-1*a*x)^5)
@test integrate((c+-1*a*c*x)^4*exp(4*arctanh(a*x)), x) == :(x*c^4+-2//3*a^2*c^4*x^3+1//5*a^4*c^4*x^5)
@test integrate((c+-1*a*c*x)^3*exp(4*arctanh(a*x)), x) == :(-1//4*a^-1*c^3*(1+a*x)^4+2//3*a^-1*c^3*(1+a*x)^3)
@test integrate((c+-1*a*c*x)^2*exp(4*arctanh(a*x)), x) == :(1//3*a^-1*c^2*(1+a*x)^3)
@test integrate((c+-1*a*c*x)*exp(4*arctanh(a*x)), x) == :(-3*c*x+-4*c*a^-1*log(1+-1*a*x)+-1//2*a*c*x^2)
@test integrate((c+-1*a*c*x)^-1*exp(4*arctanh(a*x)), x) == :(-1*a^-1*c^-1*log(1+-1*a*x)+-4*a^-1*c^-1*(1+-1*a*x)^-1+2*a^-1*c^-1*(1+-1*a*x)^-2)
@test integrate((c+-1*a*c*x)^-2*exp(4*arctanh(a*x)), x) == :(1//6*a^-1*c^-2*(1+a*x)^3*(1+-1*a*x)^-3)
@test integrate((c+-1*a*c*x)^-3*exp(4*arctanh(a*x)), x) == :(a^-1*c^-3*(1+-1*a*x)^-4+(1/2)*a^-1*c^-3*(1+-1*a*x)^-2+-4//3*a^-1*c^-3*(1+-1*a*x)^-3)
@test integrate((c+-1*a*c*x)^-4*exp(4*arctanh(a*x)), x) == :(-1*a^-1*c^-4*(1+-1*a*x)^-4+1//3*a^-1*c^-4*(1+-1*a*x)^-3+4//5*a^-1*c^-4*(1+-1*a*x)^-5)
@test integrate((c+-1*a*c*x)^3*exp(-1*arctanh(a*x)), x) == :(35//8*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)+35//8*a^-1*c^3*arcsin(a*x)+1//4*a^-1*c^3*(1+-1*a*x)^3*(1+-1*a^2*x^2)^(1/2)+7//12*a^-1*c^3*(1+-1*a*x)^2*(1+-1*a^2*x^2)^(1/2)+35//24*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate((c+-1*a*c*x)^2*exp(-1*arctanh(a*x)), x) == :(5//2*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)+5//2*a^-1*c^2*arcsin(a*x)+1//3*a^-1*c^2*(1+-1*a*x)^2*(1+-1*a^2*x^2)^(1/2)+5//6*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate((c+-1*a*c*x)*exp(-1*arctanh(a*x)), x) == :(3//2*c*a^-1*(1+-1*a^2*x^2)^(1/2)+3//2*c*a^-1*arcsin(a*x)+(1/2)*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate((c+-1*a*c*x)^-1*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-1*arcsin(a*x))
@test integrate((c+-1*a*c*x)^-2*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*a*c*x)^-3*exp(-1*arctanh(a*x)), x) == :(1//3*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+1//3*a^-1*c^-3*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*a*c*x)^-4*exp(-1*arctanh(a*x)), x) == :(1//5*a^-1*c^-4*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^(1/2)+2//15*a^-1*c^-4*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+2//15*a^-1*c^-4*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*a*c*x)^-5*exp(-1*arctanh(a*x)), x) == :(1//7*a^-1*c^-5*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^(1/2)+2//35*a^-1*c^-5*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+2//35*a^-1*c^-5*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)+3//35*a^-1*c^-5*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*a*c*x)^4*exp(-2*arctanh(a*x)), x) == :(-16*x*c^4+(1/2)*a^-1*c^4*(1+-1*a*x)^4+4*a^-1*c^4*(1+-1*a*x)^2+32*a^-1*c^4*log(1+a*x)+1//5*a^-1*c^4*(1+-1*a*x)^5+4//3*a^-1*c^4*(1+-1*a*x)^3)
@test integrate((c+-1*a*c*x)^3*exp(-2*arctanh(a*x)), x) == :(-8*x*c^3+2*a^-1*c^3*(1+-1*a*x)^2+16*a^-1*c^3*log(1+a*x)+1//4*a^-1*c^3*(1+-1*a*x)^4+2//3*a^-1*c^3*(1+-1*a*x)^3)
@test integrate((c+-1*a*c*x)^2*exp(-2*arctanh(a*x)), x) == :(-4*x*c^2+a^-1*c^2*(1+-1*a*x)^2+8*a^-1*c^2*log(1+a*x)+1//3*a^-1*c^2*(1+-1*a*x)^3)
@test integrate((c+-1*a*c*x)*exp(-2*arctanh(a*x)), x) == :(-3*c*x+(1/2)*a*c*x^2+4*c*a^-1*log(1+a*x))
@test integrate((c+-1*a*c*x)^-1*exp(-2*arctanh(a*x)), x) == :(a^-1*c^-1*log(1+a*x))
@test integrate((c+-1*a*c*x)^-2*exp(-2*arctanh(a*x)), x) == :(a^-1*c^-2*arctanh(a*x))
@test integrate((c+-1*a*c*x)^-3*exp(-2*arctanh(a*x)), x) == :((1/2)*a^-1*c^-3*(1+-1*a*x)^-1+(1/2)*a^-1*c^-3*arctanh(a*x))
@test integrate((c+-1*a*c*x)^-4*exp(-2*arctanh(a*x)), x) == :(1//4*a^-1*c^-4*(1+-1*a*x)^-1+1//4*a^-1*c^-4*(1+-1*a*x)^-2+1//4*a^-1*c^-4*arctanh(a*x))
@test integrate((c+-1*a*c*x)^-5*exp(-2*arctanh(a*x)), x) == :(1//6*a^-1*c^-5*(1+-1*a*x)^-3+1//8*a^-1*c^-5*(1+-1*a*x)^-1+1//8*a^-1*c^-5*(1+-1*a*x)^-2+1//8*a^-1*c^-5*arctanh(a*x))
@test integrate((c+-1*a*c*x)^3*exp(-3*arctanh(a*x)), x) == :(-315//8*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)+-315//8*a^-1*c^3*arcsin(a*x)+-2*a^-1*c^3*(1+-1*a*x)^5*(1+-1*a^2*x^2)^-1//2+-105//8*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x)+-21//4*a^-1*c^3*(1+-1*a*x)^2*(1+-1*a^2*x^2)^(1/2)+-9//4*a^-1*c^3*(1+-1*a*x)^3*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*a*c*x)^2*exp(-3*arctanh(a*x)), x) == :(-35//2*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)+-35//2*a^-1*c^2*arcsin(a*x)+-2*a^-1*c^2*(1+-1*a*x)^4*(1+-1*a^2*x^2)^-1//2+-35//6*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x)+-7//3*a^-1*c^2*(1+-1*a*x)^2*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*a*c*x)*exp(-3*arctanh(a*x)), x) == :(-15//2*c*a^-1*(1+-1*a^2*x^2)^(1/2)+-15//2*c*a^-1*arcsin(a*x)+-2*c*a^-1*(1+-1*a*x)^3*(1+-1*a^2*x^2)^-1//2+-5//2*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate((c+-1*a*c*x)^-1*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^-1*arcsin(a*x)+-1*a^-1*c^-1*(1+-1*a^2*x^2)^-1//2*(2+-2*a*x))
@test integrate((c+-1*a*c*x)^-2*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(1+-1*a*x))
@test integrate((c+-1*a*c*x)^-3*exp(-3*arctanh(a*x)), x) == :(x*c^-3*(1+-1*a^2*x^2)^-1//2)
@test integrate((c+-1*a*c*x)^-4*exp(-3*arctanh(a*x)), x) == :(2//3*x*c^-4*(1+-1*a^2*x^2)^-1//2+1//3*a^-1*c^-4*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^-1//2)
@test integrate((c+-1*a*c*x)^-5*exp(-3*arctanh(a*x)), x) == :(2//5*x*c^-5*(1+-1*a^2*x^2)^-1//2+1//5*a^-1*c^-5*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^-1//2+1//5*a^-1*c^-5*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^-1//2)
@test integrate((c+-1*a*c*x)^-6*exp(-3*arctanh(a*x)), x) == :(8//35*x*c^-6*(1+-1*a^2*x^2)^-1//2+1//7*a^-1*c^-6*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^-1//2+4//35*a^-1*c^-6*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^-1//2+4//35*a^-1*c^-6*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^-1//2)
@test integrate((c+-1*a*c*x)^9//2*exp(arctanh(a*x)), x) == :(2//11*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^5//2+32//99*a^-1*c^3*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^3//2+128//231*a^-1*c^4*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^(1/2)+1024//1155*a^-1*c^5*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-1//2+4096//3465*a^-1*c^6*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^7//2*exp(arctanh(a*x)), x) == :(2//9*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^3//2+8//21*a^-1*c^3*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^(1/2)+64//105*a^-1*c^4*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-1//2+256//315*a^-1*c^5*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^5//2*exp(arctanh(a*x)), x) == :(2//7*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^(1/2)+16//35*a^-1*c^3*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-1//2+64//105*a^-1*c^4*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^3//2*exp(arctanh(a*x)), x) == :(2//5*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-1//2+8//15*a^-1*c^3*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(arctanh(a*x)), x) == :(2//3*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^-1//2*exp(arctanh(a*x)), x) == :(-2*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+2*2^(1/2)*a^-1*c^-1//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^-3//2*exp(arctanh(a*x)), x) == :(a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-3//2+-1//2*2^(1/2)*a^-1*c^-3//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^-5//2*exp(arctanh(a*x)), x) == :((1/2)*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-5//2+-1//8*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-3//2+-1//16*2^(1/2)*a^-1*c^-5//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^-7//2*exp(arctanh(a*x)), x) == :(1//3*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-7//2+-1//24*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-5//2+-1//32*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-3//2+-1//64*2^(1/2)*a^-1*c^-7//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^7//2*exp(2*arctanh(a*x)), x) == :(-4//7*a^-1*(c+-1*a*c*x)^7//2+2//9*a^-1*c^-1*(c+-1*a*c*x)^9//2)
@test integrate((c+-1*a*c*x)^5//2*exp(2*arctanh(a*x)), x) == :(-4//5*a^-1*(c+-1*a*c*x)^5//2+2//7*a^-1*c^-1*(c+-1*a*c*x)^7//2)
@test integrate((c+-1*a*c*x)^3//2*exp(2*arctanh(a*x)), x) == :(-4//3*a^-1*(c+-1*a*c*x)^3//2+2//5*a^-1*c^-1*(c+-1*a*c*x)^5//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4*a^-1*(c+-1*a*c*x)^(1/2)+2//3*a^-1*c^-1*(c+-1*a*c*x)^3//2)
@test integrate((c+-1*a*c*x)^-1//2*exp(2*arctanh(a*x)), x) == :(4*a^-1*(c+-1*a*c*x)^-1//2+2*a^-1*c^-1*(c+-1*a*c*x)^(1/2))
@test integrate((c+-1*a*c*x)^-3//2*exp(2*arctanh(a*x)), x) == :(4//3*a^-1*(c+-1*a*c*x)^-3//2+-2*a^-1*c^-1*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^-5//2*exp(2*arctanh(a*x)), x) == :(4//5*a^-1*(c+-1*a*c*x)^-5//2+-2//3*a^-1*c^-1*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^-7//2*exp(2*arctanh(a*x)), x) == :(4//7*a^-1*(c+-1*a*c*x)^-7//2+-2//5*a^-1*c^-1*(c+-1*a*c*x)^-5//2)
@test integrate((c+-1*a*c*x)^9//2*exp(3*arctanh(a*x)), x) == :(2//11*a^-1*c^4*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^(1/2)+8//33*a^-1*c^5*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^-1//2+64//231*a^-1*c^6*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^-3//2+256//1155*a^-1*c^7*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^-5//2)
@test integrate((c+-1*a*c*x)^7//2*exp(3*arctanh(a*x)), x) == :(2//9*a^-1*c^4*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^-1//2+16//63*a^-1*c^5*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^-3//2+64//315*a^-1*c^6*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^-5//2)
@test integrate((c+-1*a*c*x)^5//2*exp(3*arctanh(a*x)), x) == :(2//7*a^-1*c^4*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^-3//2+8//35*a^-1*c^5*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^-5//2)
@test integrate((c+-1*a*c*x)^3//2*exp(3*arctanh(a*x)), x) == :(2//5*a^-1*c^4*(1+-1*a^2*x^2)^5//2*(c+-1*a*c*x)^-5//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+-2//3*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^-1//2*exp(3*arctanh(a*x)), x) == :(3*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-5//2+-3*2^(1/2)*a^-1*c^-1//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^-3//2*exp(3*arctanh(a*x)), x) == :(-3//4*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-3//2+(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-7//2+3//8*2^(1/2)*a^-1*c^-3//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^-5//2*exp(3*arctanh(a*x)), x) == :(-1//4*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-5//2+1//3*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-9//2+1//16*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-3//2+1//32*2^(1/2)*a^-1*c^-5//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^-7//2*exp(3*arctanh(a*x)), x) == :(-1//8*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-7//2+1//4*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-11//2+1//64*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-5//2+3//256*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-3//2+3//512*2^(1/2)*a^-1*c^-7//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^9//2*exp(-1*arctanh(a*x)), x) == :(2//11*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^9//2+40//99*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^7//2+512//231*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^3//2+640//693*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^5//2+4096//693*a^-1*c^4*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^(1/2)+16384//693*a^-1*c^5*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^7//2*exp(-1*arctanh(a*x)), x) == :(2//9*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^7//2+32//63*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^5//2+128//105*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^3//2+1024//315*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^(1/2)+4096//315*a^-1*c^4*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^5//2*exp(-1*arctanh(a*x)), x) == :(2//7*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^5//2+24//35*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^3//2+64//35*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^(1/2)+256//35*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^3//2*exp(-1*arctanh(a*x)), x) == :(2//5*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^3//2+16//15*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^(1/2)+64//15*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(-1*arctanh(a*x)), x) == :(2//3*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^(1/2)+8//3*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^-1//2*exp(-1*arctanh(a*x)), x) == :(2*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^-3//2*exp(-1*arctanh(a*x)), x) == :(2^(1/2)*a^-1*c^-3//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^-5//2*exp(-1*arctanh(a*x)), x) == :((1/2)*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-3//2+1//4*2^(1/2)*a^-1*c^-5//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^-7//2*exp(-1*arctanh(a*x)), x) == :(1//4*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-5//2+3//16*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-3//2+3//32*2^(1/2)*a^-1*c^-7//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^7//2*exp(-2*arctanh(a*x)), x) == :(4//7*a^-1*(c+-1*a*c*x)^7//2+32*a^-1*c^3*(c+-1*a*c*x)^(1/2)+2//9*a^-1*c^-1*(c+-1*a*c*x)^9//2+8//5*c*a^-1*(c+-1*a*c*x)^5//2+16//3*a^-1*c^2*(c+-1*a*c*x)^3//2+-32*2^(1/2)*a^-1*c^7//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^5//2*exp(-2*arctanh(a*x)), x) == :(4//5*a^-1*(c+-1*a*c*x)^5//2+16*a^-1*c^2*(c+-1*a*c*x)^(1/2)+2//7*a^-1*c^-1*(c+-1*a*c*x)^7//2+8//3*c*a^-1*(c+-1*a*c*x)^3//2+-16*2^(1/2)*a^-1*c^5//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^3//2*exp(-2*arctanh(a*x)), x) == :(4//3*a^-1*(c+-1*a*c*x)^3//2+8*c*a^-1*(c+-1*a*c*x)^(1/2)+2//5*a^-1*c^-1*(c+-1*a*c*x)^5//2+-8*2^(1/2)*a^-1*c^3//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(4*a^-1*(c+-1*a*c*x)^(1/2)+2//3*a^-1*c^-1*(c+-1*a*c*x)^3//2+-4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-1//2*exp(-2*arctanh(a*x)), x) == :(2*a^-1*c^-1*(c+-1*a*c*x)^(1/2)+-2*2^(1/2)*a^-1*c^-1//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-3//2*exp(-2*arctanh(a*x)), x) == :(-1*2^(1/2)*a^-1*c^-3//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-5//2*exp(-2*arctanh(a*x)), x) == :(a^-1*c^-2*(c+-1*a*c*x)^-1//2+-1//2*2^(1/2)*a^-1*c^-5//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-7//2*exp(-2*arctanh(a*x)), x) == :((1/2)*a^-1*c^-3*(c+-1*a*c*x)^-1//2+1//3*a^-1*c^-2*(c+-1*a*c*x)^-3//2+-1//4*2^(1/2)*a^-1*c^-7//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-9//2*exp(-2*arctanh(a*x)), x) == :(1//4*a^-1*c^-4*(c+-1*a*c*x)^-1//2+1//5*a^-1*c^-2*(c+-1*a*c*x)^-5//2+1//6*a^-1*c^-3*(c+-1*a*c*x)^-3//2+-1//8*2^(1/2)*a^-1*c^-9//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^5//2*exp(-3*arctanh(a*x)), x) == :(128//35*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^5//2+-4096//35*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2)+2//7*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^9//2+32//35*a^-1*c^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^7//2+1024//35*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^3//2)
@test integrate((c+-1*a*c*x)^3//2*exp(-3*arctanh(a*x)), x) == :(64//5*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^3//2+-256//5*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2)+2//5*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^7//2+8//5*a^-1*c^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^5//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-64//3*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2)+2//3*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^5//2+16//3*a^-1*c^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^3//2)
@test integrate((c+-1*a*c*x)^-1//2*exp(-3*arctanh(a*x)), x) == :(-8*a^-1*c^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2)+2*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^3//2)
@test integrate((c+-1*a*c*x)^-3//2*exp(-3*arctanh(a*x)), x) == :(-2*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate((c+-1*a*c*x)^-5//2*exp(-3*arctanh(a*x)), x) == :((1/2)*2^(1/2)*a^-1*c^-5//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+-1*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate((c+-1*a*c*x)^-7//2*exp(-3*arctanh(a*x)), x) == :((1/2)*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^-1//2+-3//4*a^-1*c^-4*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2)+3//8*2^(1/2)*a^-1*c^-7//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate((c+-1*a*c*x)^-9//2*exp(-3*arctanh(a*x)), x) == :(-15//32*a^-1*c^-5*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2)+1//4*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^-3//2+5//16*a^-1*c^-4*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^-1//2+15//64*2^(1/2)*a^-1*c^-9//2*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2))
@test integrate(x^4*(c+-1*a*c*x)*exp(arctanh(a*x)), x) == :(1//6*c*x^5*(1+-1*a^2*x^2)^(1/2)+1//16*c*a^-5*arcsin(a*x)+-1//16*c*x*a^-4*(1+-1*a^2*x^2)^(1/2)+-1//24*c*a^-2*x^3*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^3*(c+-1*a*c*x)*exp(arctanh(a*x)), x) == :(-1//3*c*a^-4*(1+-1*a^2*x^2)^3//2+1//5*c*a^-4*(1+-1*a^2*x^2)^5//2)
@test integrate(x^2*(c+-1*a*c*x)*exp(arctanh(a*x)), x) == :(1//4*c*x^3*(1+-1*a^2*x^2)^(1/2)+1//8*c*a^-3*arcsin(a*x)+-1//8*c*x*a^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*a*c*x)*exp(arctanh(a*x)), x) == :(-1//3*c*a^-2*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)*exp(arctanh(a*x)), x) == :((1/2)*c*x*(1+-1*a^2*x^2)^(1/2)+(1/2)*c*a^-1*arcsin(a*x))
@test integrate(x^-1*(c+-1*a*c*x)*exp(arctanh(a*x)), x) == :(c*(1+-1*a^2*x^2)^(1/2)+-1*c*arctanh((1+-1*a^2*x^2)^(1/2)))
@test integrate(x^-2*(c+-1*a*c*x)*exp(arctanh(a*x)), x) == :(-1*a*c*arcsin(a*x)+-1*c*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-3*(c+-1*a*c*x)*exp(arctanh(a*x)), x) == :((1/2)*c*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-4*(c+-1*a*c*x)*exp(arctanh(a*x)), x) == :(-1//3*c*x^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^3*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(-1//16*a^-4*c^2*arcsin(a*x)+-1//5*a^-2*c^2*x^2*(1+-1*a^2*x^2)^3//2+-1//16*x*a^-3*c^2*(1+-1*a^2*x^2)^(1/2)+-1//120*a^-4*c^2*(1+-1*a^2*x^2)^3//2*(16+-15*a*x)+1//6*a^-1*c^2*x^3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^2*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(-1//5*a^-3*c^2*(1+-1*a^2*x^2)^5//2+1//3*a^-3*c^2*(1+-1*a^2*x^2)^3//2+1//8*a^-3*c^2*arcsin(a*x)+-1//4*x*a^-2*c^2*(1+-1*a^2*x^2)^3//2+1//8*x*a^-2*c^2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(-1//8*a^-2*c^2*arcsin(a*x)+-1//8*x*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)+-1//12*a^-2*c^2*(1+-1*a^2*x^2)^3//2*(4+-3*a*x))
@test integrate((c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :((1/2)*x*c^2*(1+-1*a^2*x^2)^(1/2)+(1/2)*a^-1*c^2*arcsin(a*x)+1//3*a^-1*c^2*(1+-1*a^2*x^2)^3//2)
@test integrate(x^-1*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(-1*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c^2*arcsin(a*x)+(1/2)*c^2*(1+-1*a^2*x^2)^(1/2)*(2+-1*a*x))
@test integrate(x^-2*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(a*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1*a*c^2*arcsin(a*x)+-1*c^2*x^-1*(1+-1*a^2*x^2)^(1/2)*(1+a*x))
@test integrate(x^-3*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(a^2*c^2*arcsin(a*x)+(1/2)*a^2*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c^2*x^-2*(1+-1*a^2*x^2)^(1/2)*(1+-2*a*x))
@test integrate(x^-4*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(-1//2*a^3*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*c^2*x^-3*(1+-1*a^2*x^2)^3//2+(1/2)*a*c^2*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-5*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(-1//4*c^2*x^-4*(1+-1*a^2*x^2)^3//2+1//8*a^4*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//8*a^2*c^2*x^-2*(1+-1*a^2*x^2)^(1/2)+1//3*a*c^2*x^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^-6*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(-1//5*c^2*x^-5*(1+-1*a^2*x^2)^3//2+-1//8*a^5*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-2//15*a^2*c^2*x^-3*(1+-1*a^2*x^2)^3//2+1//4*a*c^2*x^-4*(1+-1*a^2*x^2)^3//2+1//8*a^3*c^2*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-7*(c+-1*a*c*x)^2*exp(arctanh(a*x)), x) == :(-1//6*c^2*x^-6*(1+-1*a^2*x^2)^3//2+1//16*a^6*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//8*a^2*c^2*x^-4*(1+-1*a^2*x^2)^3//2+-1//16*a^4*c^2*x^-2*(1+-1*a^2*x^2)^(1/2)+1//5*a*c^2*x^-5*(1+-1*a^2*x^2)^3//2+2//15*a^3*c^2*x^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^3*(c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(-1//7*c^3*x^4*(1+-1*a^2*x^2)^3//2+-1//8*a^-4*c^3*arcsin(a*x)+-11//35*a^-2*c^3*x^2*(1+-1*a^2*x^2)^3//2+-1//8*x*a^-3*c^3*(1+-1*a^2*x^2)^(1/2)+-1//420*a^-4*c^3*(1+-1*a^2*x^2)^3//2*(88+-105*a*x)+1//3*a^-1*c^3*x^3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^2*(c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(-1//6*c^3*x^3*(1+-1*a^2*x^2)^3//2+3//16*a^-3*c^3*arcsin(a*x)+1//120*a^-3*c^3*(1+-1*a^2*x^2)^3//2*(32+-45*a*x)+2//5*a^-1*c^3*x^2*(1+-1*a^2*x^2)^3//2+3//16*x*a^-2*c^3*(1+-1*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(-1//4*a^-2*c^3*arcsin(a*x)+-1//5*c^3*x^2*(1+-1*a^2*x^2)^3//2+-1//4*x*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)+-1//30*a^-2*c^3*(1+-1*a^2*x^2)^3//2*(14+-15*a*x))
@test integrate((c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(5//8*x*c^3*(1+-1*a^2*x^2)^(1/2)+5//8*a^-1*c^3*arcsin(a*x)+5//12*a^-1*c^3*(1+-1*a^2*x^2)^3//2+1//4*a^-1*c^3*(1+-1*a^2*x^2)^3//2*(1+-1*a*x))
@test integrate(x^-1*(c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(-1*c^3*arcsin(a*x)+-1*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*c^3*(1+-1*a^2*x^2)^3//2+c^3*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate(x^-2*(c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(-1*c^3*x^-1*(1+-1*a^2*x^2)^3//2+2*a*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*a*c^3*arcsin(a*x)+-1//2*a*c^3*(1+-1*a^2*x^2)^(1/2)*(4+a*x))
@test integrate(x^-3*(c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(2*a^2*c^3*arcsin(a*x)+-1//2*a^2*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c^3*x^-2*(1+-1*a^2*x^2)^3//2+(1/2)*a*c^3*x^-1*(1+-1*a^2*x^2)^(1/2)*(4+a*x))
@test integrate(x^-4*(c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(-1*a^3*c^3*arcsin(a*x)+-1*a^3*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*c^3*x^-3*(1+-1*a^2*x^2)^3//2+a*c^3*x^-2*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate(x^-5*(c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(-1//4*c^3*x^-4*(1+-1*a^2*x^2)^3//2+5//8*a^4*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-5//8*a^2*c^3*x^-2*(1+-1*a^2*x^2)^(1/2)+2//3*a*c^3*x^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^-6*(c+-1*a*c*x)^3*exp(arctanh(a*x)), x) == :(-1//4*a^5*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//5*c^3*x^-5*(1+-1*a^2*x^2)^3//2+(1/2)*a*c^3*x^-4*(1+-1*a^2*x^2)^3//2+-7//15*a^2*c^3*x^-3*(1+-1*a^2*x^2)^3//2+1//4*a^3*c^3*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^3*(c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(-29//128*a^-4*c^4*arcsin(a*x)+-3//7*c^4*x^4*(1+-1*a^2*x^2)^3//2+-29//128*x*a^-3*c^4*(1+-1*a^2*x^2)^(1/2)+-19//35*a^-2*c^4*x^2*(1+-1*a^2*x^2)^3//2+-1//6720*a^-4*c^4*(1+-1*a^2*x^2)^3//2*(2432+-3045*a*x)+1//8*a*c^4*x^5*(1+-1*a^2*x^2)^3//2+29//48*a^-1*c^4*x^3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^2*(c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(-1//2*c^4*x^3*(1+-1*a^2*x^2)^3//2+5//16*a^-3*c^4*arcsin(a*x)+1//7*a*c^4*x^4*(1+-1*a^2*x^2)^3//2+5//7*a^-1*c^4*x^2*(1+-1*a^2*x^2)^3//2+5//16*x*a^-2*c^4*(1+-1*a^2*x^2)^(1/2)+5//168*a^-3*c^4*(1+-1*a^2*x^2)^3//2*(16+-21*a*x))
@test integrate(x*(c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(-7//16*a^-2*c^4*arcsin(a*x)+-7//24*a^-2*c^4*(1+-1*a^2*x^2)^3//2+-7//16*x*a^-1*c^4*(1+-1*a^2*x^2)^(1/2)+-7//40*a^-2*c^4*(1+-1*a^2*x^2)^3//2*(1+-1*a*x)+-1//6*a^-2*c^4*(1+-1*a*x)^3*(1+-1*a^2*x^2)^3//2+-1//10*a^-2*c^4*(1+-1*a*x)^2*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(7//8*x*c^4*(1+-1*a^2*x^2)^(1/2)+7//8*a^-1*c^4*arcsin(a*x)+7//12*a^-1*c^4*(1+-1*a^2*x^2)^3//2+1//5*a^-1*c^4*(1+-1*a*x)^2*(1+-1*a^2*x^2)^3//2+7//20*a^-1*c^4*(1+-1*a^2*x^2)^3//2*(1+-1*a*x))
@test integrate(x^-1*(c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(-1*c^4*(1+-1*a^2*x^2)^3//2+-1*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-13//8*c^4*arcsin(a*x)+1//8*c^4*(1+-1*a^2*x^2)^(1/2)*(8+-13*a*x)+1//4*a*x*c^4*(1+-1*a^2*x^2)^3//2)
@test integrate(x^-2*(c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :((1/2)*a*c^4*arcsin(a*x)+-1*c^4*x^-1*(1+-1*a^2*x^2)^3//2+3*a*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+1//3*a*c^4*(1+-1*a^2*x^2)^3//2+-1//2*a*c^4*(1+-1*a^2*x^2)^(1/2)*(6+-1*a*x))
@test integrate(x^-3*(c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(-5//2*a^2*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c^4*x^-2*(1+-1*a^2*x^2)^3//2+5//2*a^2*c^4*arcsin(a*x)+3*a*c^4*x^-1*(1+-1*a^2*x^2)^3//2+5//2*a^2*c^4*(1+-1*a^2*x^2)^(1/2)*(1+a*x))
@test integrate(x^-4*(c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(-3*a^3*c^4*arcsin(a*x)+-1//2*a^3*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*c^4*x^-3*(1+-1*a^2*x^2)^3//2+3//2*a*c^4*x^-2*(1+-1*a^2*x^2)^3//2+-1//2*a^2*c^4*x^-1*(1+-1*a^2*x^2)^(1/2)*(6+-1*a*x))
@test integrate(x^-6*(c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(-7//8*a^5*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//5*c^4*x^-5*(1+-1*a^2*x^2)^3//2+-17//15*a^2*c^4*x^-3*(1+-1*a^2*x^2)^3//2+3//4*a*c^4*x^-4*(1+-1*a^2*x^2)^3//2+7//8*a^3*c^4*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-7*(c+-1*a*c*x)^4*exp(arctanh(a*x)), x) == :(-1//6*c^4*x^-6*(1+-1*a^2*x^2)^3//2+7//16*a^6*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-7//8*a^2*c^4*x^-4*(1+-1*a^2*x^2)^3//2+-7//16*a^4*c^4*x^-2*(1+-1*a^2*x^2)^(1/2)+3//5*a*c^4*x^-5*(1+-1*a^2*x^2)^3//2+11//15*a^3*c^4*x^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^4*(c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-27//8*a^-5*c^-1*arcsin(a*x)+13//3*a^-5*c^-1*(1+-1*a^2*x^2)^(1/2)+a^-5*c^-1*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+1//4*a^-2*c^-1*x^3*(1+-1*a^2*x^2)^(1/2)+2//3*a^-3*c^-1*x^2*(1+-1*a^2*x^2)^(1/2)+11//8*x*a^-4*c^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^3*(c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-3*a^-4*c^-1*arcsin(a*x)+11//3*a^-4*c^-1*(1+-1*a^2*x^2)^(1/2)+x*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)+a^-4*c^-1*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+1//3*a^-2*c^-1*x^2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^2*(c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-5//2*a^-3*c^-1*arcsin(a*x)+a^-3*c^-1*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+(1/2)*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)*(6+a*x))
@test integrate(x*(c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-2*a^-2*c^-1*arcsin(a*x)+2*a^-2*c^-1*(1+-1*a^2*x^2)^(1/2)+a^-2*c^-1*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-1*a^-1*c^-1*arcsin(a*x)+2*a^-1*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-1*(c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-1*c^-1*arctanh((1+-1*a^2*x^2)^(1/2))+c^-1*(1+-1*a^2*x^2)^-1//2*(2+2*a*x))
@test integrate(x^-2*(c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-1*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2)+-2*a*c^-1*arctanh((1+-1*a^2*x^2)^(1/2))+2*a*c^-1*(1+-1*a^2*x^2)^-1//2*(1+a*x))
@test integrate(x^-3*(c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-5//2*a^2*c^-1*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c^-1*x^-2*(1+-1*a^2*x^2)^(1/2)+-2*a*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2)+2*a^2*c^-1*(1+-1*a^2*x^2)^-1//2*(1+a*x))
@test integrate(x^-4*(c+-1*a*c*x)^-1*exp(arctanh(a*x)), x) == :(-3*a^3*c^-1*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*c^-1*x^-3*(1+-1*a^2*x^2)^(1/2)+-1*a*c^-1*x^-2*(1+-1*a^2*x^2)^(1/2)+2*a^3*c^-1*(1+-1*a^2*x^2)^-1//2*(1+a*x)+-8//3*a^2*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^4*(c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(-5//2*a^-5*c^-2*(1+-1*a^2*x^2)^(1/2)+17//2*a^-5*c^-2*arcsin(a*x)+-2*a^-5*c^-2*(1+a*x)^3*(1+-1*a^2*x^2)^-1//2+-1//3*a^-5*c^-2*(1+-1*a^2*x^2)^(1/2)*(5+a*x)^2+-1//6*a^-5*c^-2*(1+-1*a^2*x^2)^(1/2)*(5+a*x)+1//3*a^-5*c^-2*(1+a*x)^3*(1+-1*a^2*x^2)^-3//2)
@test integrate(x^3*(c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(11//2*a^-4*c^-2*arcsin(a*x)+-3*a^-4*c^-2*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+-1//2*a^-4*c^-2*(1+-1*a^2*x^2)^(1/2)*(12+a*x)+1//3*a^-4*c^-2*(1+a*x)^3*(1+-1*a^2*x^2)^-3//2)
@test integrate(x^2*(c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(3*a^-3*c^-2*arcsin(a*x)+a^-3*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2+-6*a^-3*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+1//3*a^-3*c^-2*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x*(c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(a^-2*c^-2*arcsin(a*x)+-2*a^-2*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+1//3*a^-2*c^-2*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(1//3*a^-1*c^-2*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^-1*(c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(-1*c^-2*arctanh((1+-1*a^2*x^2)^(1/2))+1//3*c^-2*(1+-1*a^2*x^2)^-3//2*(4+4*a*x)+1//3*c^-2*(1+-1*a^2*x^2)^-1//2*(3+5*a*x))
@test integrate(x^-2*(c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(-1*c^-2*x^-1*(1+-1*a^2*x^2)^(1/2)+-3*a*c^-2*arctanh((1+-1*a^2*x^2)^(1/2))+1//3*a*c^-2*(1+-1*a^2*x^2)^-1//2*(9+11*a*x)+4//3*a*c^-2*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate(x^-3*(c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(-11//2*a^2*c^-2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c^-2*x^-2*(1+-1*a^2*x^2)^(1/2)+-3*a*c^-2*x^-1*(1+-1*a^2*x^2)^(1/2)+1//3*a^2*c^-2*(1+-1*a^2*x^2)^-1//2*(15+17*a*x)+4//3*a^2*c^-2*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate(x^-4*(c+-1*a*c*x)^-2*exp(arctanh(a*x)), x) == :(-17//2*a^3*c^-2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*c^-2*x^-3*(1+-1*a^2*x^2)^(1/2)+-17//3*a^2*c^-2*x^-1*(1+-1*a^2*x^2)^(1/2)+-3//2*a*c^-2*x^-2*(1+-1*a^2*x^2)^(1/2)+1//3*a^3*c^-2*(1+-1*a^2*x^2)^-1//2*(21+23*a*x)+4//3*a^3*c^-2*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate(x^4*(c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(-19//2*a^-5*c^-3*arcsin(a*x)+(1/2)*a^-5*c^-3*(1+-1*a^2*x^2)^(1/2)*(20+a*x)+6*a^-5*c^-3*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+-19//15*a^-5*c^-3*(1+a*x)^3*(1+-1*a^2*x^2)^-3//2+1//5*a^-5*c^-3*(1+a*x)^4*(1+-1*a^2*x^2)^-5//2)
@test integrate(x^3*(c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(-4*a^-4*c^-3*arcsin(a*x)+-1*a^-4*c^-3*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2+8*a^-4*c^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-14//15*a^-4*c^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2+1//5*a^-4*c^-3*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2)
@test integrate(x^2*(c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(-1*a^-3*c^-3*arcsin(a*x)+2*a^-3*c^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-3//5*a^-3*c^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2+1//5*a^-3*c^-3*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2)
@test integrate(x*(c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(-4//15*a^-2*c^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2+1//5*a^-2*c^-3*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(1//5*a^-1*c^-3*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+1//15*a^-1*c^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^-1*(c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(-1*c^-3*arctanh((1+-1*a^2*x^2)^(1/2))+1//5*c^-3*(1+-1*a^2*x^2)^-5//2*(8+8*a*x)+1//5*c^-3*(1+-1*a^2*x^2)^-1//2*(5+8*a*x)+4//5*a*x*c^-3*(1+-1*a^2*x^2)^-3//2)
@test integrate(x^-2*(c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(-1*c^-3*x^-1*(1+-1*a^2*x^2)^(1/2)+-4*a*c^-3*arctanh((1+-1*a^2*x^2)^(1/2))+1//15*a*c^-3*(1+-1*a^2*x^2)^-1//2*(60+79*a*x)+4//15*a*c^-3*(1+-1*a^2*x^2)^-3//2*(5+8*a*x)+8//5*a*c^-3*(1+-1*a^2*x^2)^-5//2*(1+a*x))
@test integrate(x^-3*(c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(-19//2*a^2*c^-3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c^-3*x^-2*(1+-1*a^2*x^2)^(1/2)+-4*a*c^-3*x^-1*(1+-1*a^2*x^2)^(1/2)+1//15*a^2*c^-3*(1+-1*a^2*x^2)^-1//2*(135+164*a*x)+4//15*a^2*c^-3*(1+-1*a^2*x^2)^-3//2*(10+13*a*x)+8//5*a^2*c^-3*(1+-1*a^2*x^2)^-5//2*(1+a*x))
@test integrate(x^-4*(c+-1*a*c*x)^-3*exp(arctanh(a*x)), x) == :(-18*a^3*c^-3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*c^-3*x^-3*(1+-1*a^2*x^2)^(1/2)+-2*a*c^-3*x^-2*(1+-1*a^2*x^2)^(1/2)+-29//3*a^2*c^-3*x^-1*(1+-1*a^2*x^2)^(1/2)+1//5*a^3*c^-3*(1+-1*a^2*x^2)^-1//2*(80+93*a*x)+4//5*a^3*c^-3*(1+-1*a^2*x^2)^-3//2*(5+6*a*x)+8//5*a^3*c^-3*(1+-1*a^2*x^2)^-5//2*(1+a*x))
@test integrate(x^5*(c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(29//2*a^-6*c^-4*arcsin(a*x)+-10*a^-6*c^-4*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+-33//35*a^-6*c^-4*(1+a*x)^4*(1+-1*a^2*x^2)^-5//2+-1//2*a^-6*c^-4*(1+-1*a^2*x^2)^(1/2)*(30+a*x)+1//7*a^-6*c^-4*(1+a*x)^5*(1+-1*a^2*x^2)^-7//2+317//105*a^-6*c^-4*(1+a*x)^3*(1+-1*a^2*x^2)^-3//2)
@test integrate(x^4*(c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(5*a^-5*c^-4*arcsin(a*x)+a^-5*c^-4*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2+-10*a^-5*c^-4*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-26//35*a^-5*c^-4*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+1//7*a^-5*c^-4*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^3//2+184//105*a^-5*c^-4*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^3*(c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(a^-4*c^-4*arcsin(a*x)+-2*a^-4*c^-4*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-19//35*a^-4*c^-4*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+1//7*a^-4*c^-4*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^3//2+86//105*a^-4*c^-4*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^2*(c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(-12//35*a^-3*c^-4*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+1//7*a^-3*c^-4*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^3//2+23//105*a^-3*c^-4*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x*(c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(-1//7*a^-2*c^-4*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+-1//21*a^-2*c^-4*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2+1//7*a^-2*c^-4*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(1//7*a^-1*c^-4*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^3//2+2//35*a^-1*c^-4*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+2//105*a^-1*c^-4*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate(x^-1*(c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(-1*c^-4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//35*c^-4*(1+-1*a^2*x^2)^-5//2*(28+-12*a*x)+1//7*c^-4*(1+-1*a^2*x^2)^-7//2*(16+16*a*x)+1//105*c^-4*(1+-1*a^2*x^2)^-3//2*(35+83*a*x)+1//105*c^-4*(1+-1*a^2*x^2)^-1//2*(105+166*a*x))
@test integrate(x^-2*(c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(-1*c^-4*x^-1*(1+-1*a^2*x^2)^(1/2)+-5*a*c^-4*arctanh((1+-1*a^2*x^2)^(1/2))+1//105*a*c^-4*(1+-1*a^2*x^2)^-3//2*(175+307*a*x)+1//105*a*c^-4*(1+-1*a^2*x^2)^-1//2*(525+719*a*x)+4//35*a*c^-4*(1+-1*a^2*x^2)^-5//2*(7+17*a*x)+16//7*a*c^-4*(1+-1*a^2*x^2)^-7//2*(1+a*x))
@test integrate(x^-3*(c+-1*a*c*x)^-4*exp(arctanh(a*x)), x) == :(-29//2*a^2*c^-4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c^-4*x^-2*(1+-1*a^2*x^2)^(1/2)+-5*a*c^-4*x^-1*(1+-1*a^2*x^2)^(1/2)+1//105*a^2*c^-4*(1+-1*a^2*x^2)^-3//2*(455+671*a*x)+1//105*a^2*c^-4*(1+-1*a^2*x^2)^-1//2*(1470+1867*a*x)+4//35*a^2*c^-4*(1+-1*a^2*x^2)^-5//2*(21+31*a*x)+16//7*a^2*c^-4*(1+-1*a^2*x^2)^-7//2*(1+a*x))
@test integrate(x*(1+x)*exp(arctanh(x)), x) == :(-1*(1+x)^(1/2)*(1+-1x)^(1/2)+-1//3*(1+x)^3//2*(1+-1x)^(1/2)+-1//3*(1+x)^5//2*(1+-1x)^(1/2)+arcsin(x))
@test integrate((1+x)*exp(arctanh(x)), x) == :(3//2*arcsin(x)+-3//2*(1+x)^(1/2)*(1+-1x)^(1/2)+-1//2*(1+x)^3//2*(1+-1x)^(1/2))
@test integrate(x*(1+x)^2*exp(arctanh(x)), x) == :(15//8*arcsin(x)+-15//8*(1+x)^(1/2)*(1+-1x)^(1/2)+-5//8*(1+x)^3//2*(1+-1x)^(1/2)+-1//4*(1+x)^5//2*(1+-1x)^(1/2)+-1//4*(1+x)^7//2*(1+-1x)^(1/2))
@test integrate((1+x)^2*exp(arctanh(x)), x) == :(5//2*arcsin(x)+-5//2*(1+x)^(1/2)*(1+-1x)^(1/2)+-5//6*(1+x)^3//2*(1+-1x)^(1/2)+-1//3*(1+x)^5//2*(1+-1x)^(1/2))
@test integrate(x*(1+x)^-1*exp(arctanh(x)), x) == :(-1*(1+x)^(1/2)*(1+-1x)^(1/2))
@test integrate((1+x)^-1*exp(arctanh(x)), x) == :(arcsin(x))
@test integrate(x*(1+x)^-2*exp(arctanh(x)), x) == :((1+x)^-1//2*(1+-1x)^(1/2)+arcsin(x))
@test integrate((1+x)^-2*exp(arctanh(x)), x) == :(-1*(1+x)^-1//2*(1+-1x)^(1/2))
@test integrate(x*(1+x)^3//2*exp(arctanh(x)), x) == :(-8*(1+-1x)^(1/2)+-2*(1+-1x)^5//2+2//7*(1+-1x)^7//2+16//3*(1+-1x)^3//2)
@test integrate((1+x)^3//2*exp(arctanh(x)), x) == :(-8*(1+-1x)^(1/2)+-2//5*(1+-1x)^5//2+8//3*(1+-1x)^3//2)
@test integrate((1+-1x)^3//2*exp(arctanh(x)), x) == :(-2//5*(1+x)^5//2+4//3*(1+x)^3//2)
@test integrate(x*(1+x)^(1/2)*exp(arctanh(x)), x) == :(-4*(1+-1x)^(1/2)+2*(1+-1x)^3//2+-2//5*(1+-1x)^5//2)
@test integrate((1+x)^(1/2)*exp(arctanh(x)), x) == :(-4*(1+-1x)^(1/2)+2//3*(1+-1x)^3//2)
@test integrate(x*(1+-1x)^(1/2)*exp(arctanh(x)), x) == :(-2//3*(1+x)^3//2+2//5*(1+x)^5//2)
@test integrate((1+-1x)^(1/2)*exp(arctanh(x)), x) == :(2//3*(1+x)^3//2)
@test integrate(x*(1+x)^-1//2*exp(arctanh(x)), x) == :(-2*(1+-1x)^(1/2)+2//3*(1+-1x)^3//2)
@test integrate((1+x)^-1//2*exp(arctanh(x)), x) == :(-2*(1+-1x)^(1/2))
@test integrate(x*(1+-1x)^-1//2*exp(arctanh(x)), x) == :(-2*(1+x)^(1/2)+-2//3*(1+x)^3//2+2*2^(1/2)*arctanh((1/2)*2^(1/2)*(1+x)^(1/2)))
@test integrate((1+-1x)^-1//2*exp(arctanh(x)), x) == :(-2*(1+x)^(1/2)+2*2^(1/2)*arctanh((1/2)*2^(1/2)*(1+x)^(1/2)))
@test integrate(x*(1+x)^-3//2*exp(arctanh(x)), x) == :(-2*(1+-1x)^(1/2)+2^(1/2)*arctanh((1/2)*2^(1/2)*(1+-1x)^(1/2)))
@test integrate((1+x)^-3//2*exp(arctanh(x)), x) == :(-1*2^(1/2)*arctanh((1/2)*2^(1/2)*(1+-1x)^(1/2)))
@test integrate(x*(1+-1x)^-3//2*exp(arctanh(x)), x) == :(5//2*(1+x)^(1/2)+(1+x)^3//2*(2+-2x)^-1+-5//2*2^(1/2)*arctanh((1/2)*2^(1/2)*(1+x)^(1/2)))
@test integrate((1+-1x)^-3//2*exp(arctanh(x)), x) == :((1+x)^(1/2)*(1+-1x)^-1+-1//2*2^(1/2)*arctanh((1/2)*2^(1/2)*(1+x)^(1/2)))
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(arctanh(a*x)), x) == :(-8//105*a^-3*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2+8//35*c*a^-3*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-1//2+2//7*a^-1*c^2*x^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(arctanh(a*x)), x) == :(-2//5*c*a^-2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-1//2+2//15*a^-2*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(arctanh(a*x)), x) == :(2//3*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(arctanh(a*x)), x) == :(-2*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+2*c*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(arctanh(a*x)), x) == :(-1*a*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+-1*c*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate(x^3*(c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4*a^-4*(c+-1*a*c*x)^(1/2)+-18//5*a^-4*c^-2*(c+-1*a*c*x)^5//2+-2//9*a^-4*c^-4*(c+-1*a*c*x)^9//2+10//7*a^-4*c^-3*(c+-1*a*c*x)^7//2+14//3*a^-4*c^-1*(c+-1*a*c*x)^3//2)
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4*a^-3*(c+-1*a*c*x)^(1/2)+-8//5*a^-3*c^-2*(c+-1*a*c*x)^5//2+2//7*a^-3*c^-3*(c+-1*a*c*x)^7//2+10//3*a^-3*c^-1*(c+-1*a*c*x)^3//2)
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4*a^-2*(c+-1*a*c*x)^(1/2)+2*a^-2*c^-1*(c+-1*a*c*x)^3//2+-2//5*a^-2*c^-2*(c+-1*a*c*x)^5//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4*a^-1*(c+-1*a*c*x)^(1/2)+2//3*a^-1*c^-1*(c+-1*a*c*x)^3//2)
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-2*(c+-1*a*c*x)^(1/2)+-2*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*x^-1*(c+-1*a*c*x)^(1/2)+-3*a*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-3*(c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//2*x^-2*(c+-1*a*c*x)^(1/2)+-7//4*a*x^-1*(c+-1*a*c*x)^(1/2)+-7//4*a^2*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-4*(c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//3*x^-3*(c+-1*a*c*x)^(1/2)+-11//8*a^2*x^-1*(c+-1*a*c*x)^(1/2)+-11//8*a^3*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+-11//12*a*x^-2*(c+-1*a*c*x)^(1/2))
@test integrate(x^-5*(c+-1*a*c*x)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//4*x^-4*(c+-1*a*c*x)^(1/2)+-75//64*a^3*x^-1*(c+-1*a*c*x)^(1/2)+-75//64*a^4*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+-25//32*a^2*x^-2*(c+-1*a*c*x)^(1/2)+-5//8*a*x^-3*(c+-1*a*c*x)^(1/2))
@test integrate(x^3*(c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*a^-4*c^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-2//3*a^-4*c^-1*(1+a*x)^3//2*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-2//5*a^-4*c^-1*(1+a*x)^5//2*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-2//9*a^-4*c^-1*(1+a*x)^9//2*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+2//7*a^-4*c^-1*(1+a*x)^7//2*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+4*2^(1/2)*a^-4*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1/2)*2^(1/2)*(1+a*x)^(1/2)))
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*a^-3*c^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-2//3*a^-3*c^-1*(1+a*x)^3//2*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-2//7*a^-3*c^-1*(1+a*x)^7//2*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+4*2^(1/2)*a^-3*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1/2)*2^(1/2)*(1+a*x)^(1/2)))
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*a^-2*c^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-2//3*a^-2*c^-1*(1+a*x)^3//2*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-2//5*a^-2*c^-1*(1+a*x)^5//2*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+4*2^(1/2)*a^-2*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1/2)*2^(1/2)*(1+a*x)^(1/2)))
@test integrate((c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+-2//3*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-2*c^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-2*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1+a*x)^(1/2))+4*2^(1/2)*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1/2)*2^(1/2)*(1+a*x)^(1/2)))
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1*c^-1*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-5*a*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1+a*x)^(1/2))+4*a*2^(1/2)*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1/2)*2^(1/2)*(1+a*x)^(1/2)))
@test integrate(x^-3*(c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-23//4*a^2*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1+a*x)^(1/2))+-1//2*c^-1*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+4*2^(1/2)*a^2*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1/2)*2^(1/2)*(1+a*x)^(1/2))+-9//4*a*c^-1*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2)
@test integrate(x^-4*(c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-45//8*a^3*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1+a*x)^(1/2))+-1//3*c^-1*x^-3*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+4*2^(1/2)*a^3*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1/2)*2^(1/2)*(1+a*x)^(1/2))+-19//8*a^2*c^-1*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-13//12*a*c^-1*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2)
@test integrate(x^-5*(c+-1*a*c*x)^(1/2)*exp(3*arctanh(a*x)), x) == :(-363//64*a^4*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1+a*x)^(1/2))+-1//4*c^-1*x^-4*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+4*2^(1/2)*a^4*c^-1*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2*arctanh((1/2)*2^(1/2)*(1+a*x)^(1/2))+-149//64*a^3*c^-1*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-107//96*a^2*c^-1*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2+-17//24*a*c^-1*x^-3*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*a*c*x)^3//2)
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(-1*arctanh(a*x)), x) == :(104//105*a^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^(1/2)+-2//7*c*x^3*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+104//105*c*a^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+26//35*c*a^-1*x^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-2//5*a^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^(1/2)+-8//5*c*a^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+-2//5*a^-2*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^3//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(-1*arctanh(a*x)), x) == :(2//3*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^(1/2)+8//3*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-2*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+-2*c*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(-1*arctanh(a*x)), x) == :(3*a*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+-1*c*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate(x^-3*(c+-1*a*c*x)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-7//4*a^2*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+-1//2*c*x^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+7//4*a*c*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate(x^-4*(c+-1*a*c*x)^(1/2)*exp(-1*arctanh(a*x)), x) == :(11//8*a^3*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)+-1//3*c*x^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+-11//8*c*a^2*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2+11//12*a*c*x^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate(x^3*(c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-4*a^-4*(c+-1*a*c*x)^(1/2)+-2//3*a^-4*c^-1*(c+-1*a*c*x)^3//2+-2//5*a^-4*c^-2*(c+-1*a*c*x)^5//2+-2//9*a^-4*c^-4*(c+-1*a*c*x)^9//2+2//7*a^-4*c^-3*(c+-1*a*c*x)^7//2+4*2^(1/2)*a^-4*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(4*a^-3*(c+-1*a*c*x)^(1/2)+2//3*a^-3*c^-1*(c+-1*a*c*x)^3//2+2//7*a^-3*c^-3*(c+-1*a*c*x)^7//2+-4*2^(1/2)*a^-3*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-4*a^-2*(c+-1*a*c*x)^(1/2)+-2//3*a^-2*c^-1*(c+-1*a*c*x)^3//2+-2//5*a^-2*c^-2*(c+-1*a*c*x)^5//2+4*2^(1/2)*a^-2*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(4*a^-1*(c+-1*a*c*x)^(1/2)+2//3*a^-1*c^-1*(c+-1*a*c*x)^3//2+-4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-2*(c+-1*a*c*x)^(1/2)+-2*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+4*2^(1/2)*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*x^-1*(c+-1*a*c*x)^(1/2)+5*a*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+-4*a*2^(1/2)*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-3*(c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//2*x^-2*(c+-1*a*c*x)^(1/2)+-23//4*a^2*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+9//4*a*x^-1*(c+-1*a*c*x)^(1/2)+4*2^(1/2)*a^2*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-4*(c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//3*x^-3*(c+-1*a*c*x)^(1/2)+-19//8*a^2*x^-1*(c+-1*a*c*x)^(1/2)+13//12*a*x^-2*(c+-1*a*c*x)^(1/2)+45//8*a^3*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+-4*2^(1/2)*a^3*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-5*(c+-1*a*c*x)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//4*x^-4*(c+-1*a*c*x)^(1/2)+-363//64*a^4*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+-107//96*a^2*x^-2*(c+-1*a*c*x)^(1/2)+17//24*a*x^-3*(c+-1*a*c*x)^(1/2)+149//64*a^3*x^-1*(c+-1*a*c*x)^(1/2)+4*2^(1/2)*a^4*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^3*(c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-2*a^-4*c^2*(1+a*x)^7//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+8*a^-4*c^2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+32*a^-4*c^2*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+-50//3*a^-4*c^2*(1+a*x)^3//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+2//9*a^-4*c^2*(1+a*x)^9//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+38//5*a^-4*c^2*(1+a*x)^5//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-24*a^-3*c^2*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+-8*a^-3*c^2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+-12//5*a^-3*c^2*(1+a*x)^5//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+2//7*a^-3*c^2*(1+a*x)^7//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+26//3*a^-3*c^2*(1+a*x)^3//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(8*a^-2*c^2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+16*a^-2*c^2*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+-10//3*a^-2*c^2*(1+a*x)^3//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+2//5*a^-2*c^2*(1+a*x)^5//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-64//3*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^(1/2)+2//3*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^5//2+16//3*a^-1*c^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*a*c*x)^3//2)
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-2*c^2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2*arctanh((1+a*x)^(1/2))+2*c^2*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+8*c^2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1*c^2*x^-1*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+-9*a*c^2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+7*a*c^2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2*arctanh((1+a*x)^(1/2)))
@test integrate(x^-3*(c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-47//4*a^2*c^2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2*arctanh((1+a*x)^(1/2))+-1//2*c^2*x^-2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+47//4*a^2*c^2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+13//4*a*c^2*x^-1*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate(x^-4*(c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-119//8*a^3*c^2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+-1//3*c^2*x^-3*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+119//8*a^3*c^2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2*arctanh((1+a*x)^(1/2))+-119//24*a^2*c^2*x^-1*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+19//12*a*c^2*x^-2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate(x^-5*(c+-1*a*c*x)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1115//64*a^4*c^2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2*arctanh((1+a*x)^(1/2))+-1//4*c^2*x^-4*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+1115//64*a^4*c^2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+-223//96*a^2*c^2*x^-2*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+25//24*a*c^2*x^-3*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2+1115//192*a^3*c^2*x^-1*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^p*exp(2*p*arctanh(a*x)), x) == :(a^-1*(1+p)^-1*(1+a*x)^(1+p)*(1+-1*a*x)^(-1p)*(c+-1*a*c*x)^p)
@test integrate((c+-1*a*c*x)^-2*exp(n*arctanh(a*x)), x) == :(a^-1*c^-2*(1+a*x)^(1+(1/2)*n)*(1+-1*a*x)^(-1+-1//2*n)*(2+n)^-1)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(arctanh(a*x)), x) == :(-3*a^-1*c^4*arcsin(a*x)+-1//2*a^-1*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*a^-4*c^4*x^-3*(1+-1*a^2*x^2)^3//2+3//2*a^-3*c^4*x^-2*(1+-1*a^2*x^2)^3//2+-1//2*a^-2*c^4*x^-1*(1+-1*a^2*x^2)^(1/2)*(6+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(arctanh(a*x)), x) == :((1/2)*a^-1*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-2*a^-1*c^3*arcsin(a*x)+(1/2)*a^-3*c^3*x^-2*(1+-1*a^2*x^2)^3//2+-1//2*a^-2*c^3*x^-1*(1+-1*a^2*x^2)^(1/2)*(4+a*x))
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(arctanh(a*x)), x) == :(a^-1*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1*a^-1*c^2*arcsin(a*x)+-1*a^-2*c^2*x^-1*(1+-1*a^2*x^2)^(1/2)*(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)*exp(arctanh(a*x)), x) == :(c*a^-1*arctanh((1+-1*a^2*x^2)^(1/2))+-1*c*a^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(arctanh(a*x)), x) == :(-2*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)+2*a^-1*c^-1*arcsin(a*x)+-1*a^-1*c^-1*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(arctanh(a*x)), x) == :(3*a^-1*c^-2*arcsin(a*x)+a^-1*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2+-6*a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+1//3*a^-1*c^-2*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(arctanh(a*x)), x) == :(4*a^-1*c^-3*arcsin(a*x)+a^-1*c^-3*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2+-8*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-1//5*a^-1*c^-3*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+14//15*a^-1*c^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(arctanh(a*x)), x) == :(5*a^-1*c^-4*arcsin(a*x)+a^-1*c^-4*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2+-10*a^-1*c^-4*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-26//35*a^-1*c^-4*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^3//2+1//7*a^-1*c^-4*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^3//2+184//105*a^-1*c^-4*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^5*exp(2*arctanh(a*x)), x) == :(-1*x*c^5+a^-3*c^5*x^-2+-1*a^-4*c^5*x^-3+2*a^-2*c^5*x^-1+3*a^-1*c^5*log(x)+1//4*a^-5*c^5*x^-4)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(2*arctanh(a*x)), x) == :(-1*x*c^4+a^-3*c^4*x^-2+2*a^-1*c^4*log(x)+-1//3*a^-4*c^4*x^-3)
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(2*arctanh(a*x)), x) == :(-1*x*c^3+a^-1*c^3*log(x)+(1/2)*a^-3*c^3*x^-2+-1*a^-2*c^3*x^-1)
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(2*arctanh(a*x)), x) == :(-1*x*c^2+-1*a^-2*c^2*x^-1)
@test integrate((c+-1*c*a^-1*x^-1)*exp(2*arctanh(a*x)), x) == :(-1*c*x+-1*c*a^-1*log(x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(2*arctanh(a*x)), x) == :(-1*x*c^-1+-3*a^-1*c^-1*log(1+-1*a*x)+-2*a^-1*c^-1*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(2*arctanh(a*x)), x) == :(-1*x*c^-2+a^-1*c^-2*(1+-1*a*x)^-2+-5*a^-1*c^-2*(1+-1*a*x)^-1+-4*a^-1*c^-2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(2*arctanh(a*x)), x) == :(-1*x*c^-3+-9*a^-1*c^-3*(1+-1*a*x)^-1+-5*a^-1*c^-3*log(1+-1*a*x)+-2//3*a^-1*c^-3*(1+-1*a*x)^-3+7//2*a^-1*c^-3*(1+-1*a*x)^-2)
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(2*arctanh(a*x)), x) == :(-1*x*c^-4+(1/2)*a^-1*c^-4*(1+-1*a*x)^-4+-14*a^-1*c^-4*(1+-1*a*x)^-1+-6*a^-1*c^-4*log(1+-1*a*x)+-3*a^-1*c^-4*(1+-1*a*x)^-3+8*a^-1*c^-4*(1+-1*a*x)^-2)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(3*arctanh(a*x)), x) == :(a^-1*c^4*arcsin(a*x)+-3//2*a^-1*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+(1/2)*a^-2*c^4*x^-1*(1+-1*a^2*x^2)^(1/2)*(2+3*a*x)+-1//6*a^-4*c^4*x^-3*(1+-1*a^2*x^2)^3//2*(2+-3*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(3*arctanh(a*x)), x) == :(-3//2*a^-1*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+3//2*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)+(1/2)*a^-3*c^3*x^-2*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(3*arctanh(a*x)), x) == :(-1*a^-1*c^2*arcsin(a*x)+-1*a^-1*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1*a^-2*c^2*x^-1*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)*exp(3*arctanh(a*x)), x) == :(c*a^-1*(1+-1*a^2*x^2)^(1/2)+c*a^-1*arctanh((1+-1*a^2*x^2)^(1/2))+-2*c*a^-1*arcsin(a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(3*arctanh(a*x)), x) == :(-4*a^-1*c^-1*arcsin(a*x)+4*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)+-1//3*a^-1*c^-1*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^5//2+8//3*a^-1*c^-1*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(3*arctanh(a*x)), x) == :(-5*a^-1*c^-2*arcsin(a*x)+5*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)+-2//3*a^-1*c^-2*(1+a*x)^4*(1+-1*a^2*x^2)^-3//2+1//5*a^-1*c^-2*(1+a*x)^5*(1+-1*a^2*x^2)^-5//2+10//3*a^-1*c^-2*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(3*arctanh(a*x)), x) == :(-6*a^-1*c^-3*arcsin(a*x)+6*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)+-1*a^-1*c^-3*(1+a*x)^4*(1+-1*a^2*x^2)^-3//2+4*a^-1*c^-3*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+-1//7*a^-1*c^-3*(1+a*x)^6*(1+-1*a^2*x^2)^-7//2+4//7*a^-1*c^-3*(1+a*x)^5*(1+-1*a^2*x^2)^-5//2)
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(3*arctanh(a*x)), x) == :(-7*a^-1*c^-4*arcsin(a*x)+7*a^-1*c^-4*(1+-1*a^2*x^2)^(1/2)+-34//63*a^-1*c^-4*(1+a*x)^6*(1+-1*a^2*x^2)^-7//2+-4//3*a^-1*c^-4*(1+a*x)^4*(1+-1*a^2*x^2)^-3//2+1//9*a^-1*c^-4*(1+a*x)^7*(1+-1*a^2*x^2)^-9//2+14//3*a^-1*c^-4*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+344//315*a^-1*c^-4*(1+a*x)^5*(1+-1*a^2*x^2)^-5//2)
@test integrate((c+-1*c*a^-1*x^-1)^5*exp(4*arctanh(a*x)), x) == :(x*c^5+-1*a^-1*c^5*log(x)+-1*a^-3*c^5*x^-2+2*a^-2*c^5*x^-1+-1//3*a^-4*c^5*x^-3+1//4*a^-5*c^5*x^-4)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(4*arctanh(a*x)), x) == :(x*c^4+2*a^-2*c^4*x^-1+-1//3*a^-4*c^4*x^-3)
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(4*arctanh(a*x)), x) == :(x*c^3+a^-1*c^3*log(x)+a^-2*c^3*x^-1+(1/2)*a^-3*c^3*x^-2)
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(4*arctanh(a*x)), x) == :(x*c^2+-1*a^-2*c^2*x^-1+2*a^-1*c^2*log(x))
@test integrate((c+-1*c*a^-1*x^-1)*exp(4*arctanh(a*x)), x) == :(c*x+-1*c*a^-1*log(x)+4*c*a^-1*log(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(4*arctanh(a*x)), x) == :(x*c^-1+-2*a^-1*c^-1*(1+-1*a*x)^-2+5*a^-1*c^-1*log(1+-1*a*x)+8*a^-1*c^-1*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(4*arctanh(a*x)), x) == :(x*c^-2+-6*a^-1*c^-2*(1+-1*a*x)^-2+6*a^-1*c^-2*log(1+-1*a*x)+13*a^-1*c^-2*(1+-1*a*x)^-1+4//3*a^-1*c^-2*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(4*arctanh(a*x)), x) == :(x*c^-3+-1*a^-1*c^-3*(1+-1*a*x)^-4+7*a^-1*c^-3*log(1+-1*a*x)+19*a^-1*c^-3*(1+-1*a*x)^-1+-25//2*a^-1*c^-3*(1+-1*a*x)^-2+16//3*a^-1*c^-3*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(4*arctanh(a*x)), x) == :(x*c^-4+-22*a^-1*c^-4*(1+-1*a*x)^-2+-5*a^-1*c^-4*(1+-1*a*x)^-4+8*a^-1*c^-4*log(1+-1*a*x)+26*a^-1*c^-4*(1+-1*a*x)^-1+4//5*a^-1*c^-4*(1+-1*a*x)^-5+41//3*a^-1*c^-4*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(-1*arctanh(a*x)), x) == :(a^-1*c^4*(1+-1*a^2*x^2)^(1/2)+5*a^-1*c^4*arcsin(a*x)+25//2*a^-1*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-32//3*a^-2*c^4*x^-1*(1+-1*a^2*x^2)^(1/2)+-1//3*a^-4*c^4*x^-3*(1+-1*a^2*x^2)^(1/2)+5//2*a^-3*c^4*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(-1*arctanh(a*x)), x) == :(a^-1*c^3*(1+-1*a^2*x^2)^(1/2)+4*a^-1*c^3*arcsin(a*x)+13//2*a^-1*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+(1/2)*a^-3*c^3*x^-2*(1+-1*a^2*x^2)^(1/2)+-4*a^-2*c^3*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(-1*arctanh(a*x)), x) == :(a^-1*c^2*(1+-1*a^2*x^2)^(1/2)+3*a^-1*c^2*arcsin(a*x)+3*a^-1*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1*a^-2*c^2*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)*exp(-1*arctanh(a*x)), x) == :(c*a^-1*(1+-1*a^2*x^2)^(1/2)+c*a^-1*arctanh((1+-1*a^2*x^2)^(1/2))+2*c*a^-1*arcsin(a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)+-1*a^-1*c^-2*arcsin(a*x)+a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)+-2*a^-1*c^-3*arcsin(a*x)+-1//3*a^-1*c^-3*(1+a*x)^2*(1+-1*a^2*x^2)^-3//2+1//3*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(8+8*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-4*(1+-1*a^2*x^2)^(1/2)+-3*a^-1*c^-4*arcsin(a*x)+-6//5*a^-1*c^-4*(1+a*x)^2*(1+-1*a^2*x^2)^-3//2+1//5*a^-1*c^-4*(1+a*x)^3*(1+-1*a^2*x^2)^-5//2+1//5*a^-1*c^-4*(1+-1*a^2*x^2)^-1//2*(24+24*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(-2*arctanh(a*x)), x) == :(-1*x*c^4+-26*a^-1*c^4*log(x)+-16*a^-2*c^4*x^-1+3*a^-3*c^4*x^-2+32*a^-1*c^4*log(1+a*x)+-1//3*a^-4*c^4*x^-3)
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(-2*arctanh(a*x)), x) == :(-1*x*c^3+(1/2)*a^-3*c^3*x^-2+-11*a^-1*c^3*log(x)+-5*a^-2*c^3*x^-1+16*a^-1*c^3*log(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(-2*arctanh(a*x)), x) == :(-1*x*c^2+-1*a^-2*c^2*x^-1+-4*a^-1*c^2*log(x)+8*a^-1*c^2*log(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)*exp(-2*arctanh(a*x)), x) == :(-1*c*x+-1*c*a^-1*log(x)+4*c*a^-1*log(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-1+a^-1*c^-1*log(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-2+a^-1*c^-2*arctanh(a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-3+-5//4*a^-1*c^-3*log(1+-1*a*x)+-1//2*a^-1*c^-3*(1+-1*a*x)^-1+1//4*a^-1*c^-3*log(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-4+-17//8*a^-1*c^-4*log(1+-1*a*x)+-7//4*a^-1*c^-4*(1+-1*a*x)^-1+1//4*a^-1*c^-4*(1+-1*a*x)^-2+1//8*a^-1*c^-4*log(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)+-6*a^-1*c^3*arcsin(a*x)+33//2*a^-1*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+(1/2)*a^-3*c^3*x^-2*(1+-1*a^2*x^2)^(1/2)+-32*a^-1*c^3*(1+-1*a^2*x^2)^-1//2*(1+-1*a*x)+-6*a^-2*c^3*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)+-5*a^-1*c^2*arcsin(a*x)+5*a^-1*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1*a^-2*c^2*x^-1*(1+-1*a^2*x^2)^(1/2)+-16*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)*exp(-3*arctanh(a*x)), x) == :(c*a^-1*arctanh((1+-1*a^2*x^2)^(1/2))+-1*c*a^-1*(1+-1*a^2*x^2)^(1/2)+-4*c*a^-1*arcsin(a*x)+-8*c*a^-1*(1+-1*a^2*x^2)^-1//2*(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(-3*arctanh(a*x)), x) == :(-2*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)+-2*a^-1*c^-1*arcsin(a*x)+-1*a^-1*c^-1*(1+-1*a*x)^2*(1+-1*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)+-1*a^-1*c^-2*arcsin(a*x)+-1*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)+-1*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(-3*arctanh(a*x)), x) == :(a^-1*c^-4*arcsin(a*x)+-8//3*a^-1*c^-4*(1+-1*a^2*x^2)^(1/2)+-1//3*x*c^-4*(1+-1*a^2*x^2)^-1//2*(3+4*a*x)+1//3*a^2*c^-4*x^3*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-5*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^-5*(1+-1*a^2*x^2)^(1/2)+2*a^-1*c^-5*arcsin(a*x)+-1//5*a^-1*c^-5*(1+a*x)^2*(1+-1*a^2*x^2)^-5//2+-1//15*a^-1*c^-5*(1+-1*a^2*x^2)^-1//2*(60+46*a*x)+1//15*a^-1*c^-5*(1+-1*a^2*x^2)^-3//2*(22+22*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^9//2*exp(arctanh(a*x)), x) == :(-2//7*x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^9//2+-7*a^7//2*x^9//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*arcsinh(a^(1/2)*x^(1/2))+-10//21*a^2*x^3*(1+a*x)^(1/2)*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^9//2+2//5*a*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^9//2+-1//105*a^3*x^4*(1+a*x)^(1/2)*(1+-1*a*x)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*(54+-227*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(arctanh(a*x)), x) == :(-2//5*x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^7//2+5*a^5//2*x^7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*arcsinh(a^(1/2)*x^(1/2))+2//3*a*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^7//2+-1//15*a^2*x^3*(1+a*x)^(1/2)*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*(18+31*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(arctanh(a*x)), x) == :(-2//3*x*(1+a*x)^3//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2+-3*a^2*x^3*(1+a*x)^(1/2)*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2+-3*a^3//2*x^5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*arcsinh(a^(1/2)*x^(1/2))+4*a*x^2*(1+a*x)^3//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(arctanh(a*x)), x) == :(-2*x*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-1*x^-1)^3//2+a*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2+a^(1/2)*x^3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2*arcsinh(a^(1/2)*x^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(arctanh(a*x)), x) == :(-1*a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-3*a^-3//2*x^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arcsinh(a^(1/2)*x^(1/2))+2*2^(1/2)*a^-3//2*x^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(arctanh(a*x)), x) == :(a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-3//2+2*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+5*a^-5//2*x^-3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arcsinh(a^(1/2)*x^(1/2))+-7//2*2^(1/2)*a^-5//2*x^-3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(arctanh(a*x)), x) == :((1/2)*a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-5//2+-7*a^-7//2*x^-5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arcsinh(a^(1/2)*x^(1/2))+-23//8*a^-3*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2+-11//8*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-5//2+79//16*2^(1/2)*a^-7//2*x^-5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^9//2*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^9//2+-1*a^-1*c^2*(c+-1*c*a^-1*x^-1)^5//2+-5*a^-1*c^4*(c+-1*c*a^-1*x^-1)^(1/2)+5*a^-1*c^9//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-5//3*a^-1*c^3*(c+-1*c*a^-1*x^-1)^3//2+-5//7*c*a^-1*(c+-1*c*a^-1*x^-1)^7//2)
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^7//2+-1*a^-1*c^2*(c+-1*c*a^-1*x^-1)^3//2+-3*a^-1*c^3*(c+-1*c*a^-1*x^-1)^(1/2)+3*a^-1*c^7//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-3//5*c*a^-1*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^5//2+a^-1*c^5//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-1*a^-1*c^2*(c+-1*c*a^-1*x^-1)^(1/2)+-1//3*c*a^-1*(c+-1*c*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^3//2+c*a^-1*(c+-1*c*a^-1*x^-1)^(1/2)+-1*a^-1*c^3//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^(1/2)+-3*a^-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^-1//2+5*a^-1*(c+-1*c*a^-1*x^-1)^-1//2+-5*a^-1*c^-1//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^-3//2+7//3*a^-1*(c+-1*c*a^-1*x^-1)^-3//2+-7*a^-1*c^-3//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+7*a^-1*c^-1*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^-5//2+9//5*a^-1*(c+-1*c*a^-1*x^-1)^-5//2+-9*a^-1*c^-5//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+3*a^-1*c^-1*(c+-1*c*a^-1*x^-1)^-3//2+9*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-7//2*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^-7//2+11//7*a^-1*(c+-1*c*a^-1*x^-1)^-7//2+-11*a^-1*c^-7//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+11*a^-1*c^-3*(c+-1*c*a^-1*x^-1)^-1//2+11//3*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-3//2+11//5*a^-1*c^-1*(c+-1*c*a^-1*x^-1)^-5//2)
@test integrate((c+-1*c*a^-1*x^-1)^9//2*exp(3*arctanh(a*x)), x) == :(-2//7*x*(1+a*x)^3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^9//2+-3*a^3*x^4*(1+a*x)^(1/2)*(1+-1*a*x)^-9//2*(c+-1*c*a^-1*x^-1)^9//2+3*a^7//2*x^9//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*arcsinh(a^(1/2)*x^(1/2))+6//35*a*x^2*(1+a*x)^3//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^9//2+3//35*a^2*x^3*(1+a*x)^3//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*(6+-17*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(3*arctanh(a*x)), x) == :(-2//5*x*(1+a*x)^5//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2+-1*a^3*x^4*(1+a*x)^(1/2)*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2+-1*a^5//2*x^7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*arcsinh(a^(1/2)*x^(1/2))+2//3*a^2*x^3*(1+a*x)^3//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2+4//3*a*x^2*(1+a*x)^5//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2)
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(3*arctanh(a*x)), x) == :(-2//3*x*(1+-1*a*x)^-5*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-1*x^-1)^5//2+-1*a^2*x^3*(1+a*x)^(1/2)*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2+-1*a^3//2*x^5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*arcsinh(a^(1/2)*x^(1/2))+2//3*a*x^2*(1+a*x)^3//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(3*arctanh(a*x)), x) == :(-2*x*(1+a*x)^3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2+3*a*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2+3*a^(1/2)*x^3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2*arcsinh(a^(1/2)*x^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1*x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-5*a^-1//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+4*2^(1/2)*a^-1//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(3*arctanh(a*x)), x) == :(a^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^-1//2+2*a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+7*a^-3//2*x^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arcsinh(a^(1/2)*x^(1/2))+-5*2^(1/2)*a^-3//2*x^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(3*arctanh(a*x)), x) == :((1/2)*a^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^-3//2+-9*a^-5//2*x^-3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arcsinh(a^(1/2)*x^(1/2))+-21//8*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+-9//8*a^-2*x^-1*(1+a*x)^3//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-3//2+51//8*2^(1/2)*a^-5//2*x^-3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(3*arctanh(a*x)), x) == :(1//3*a^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^-5//2+11*a^-7//2*x^-5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arcsinh(a^(1/2)*x^(1/2))+-13//24*a^-2*x^-1*(1+a*x)^3//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-5//2+43//32*a^-3*x^-2*(1+a*x)^3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-5//2+103//32*a^-3*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2+-249//32*2^(1/2)*a^-7//2*x^-5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^9//2*exp(-1*arctanh(a*x)), x) == :(-2//7*x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^9//2+11*a^7//2*x^9//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*arcsinh(a^(1/2)*x^(1/2))+-94//21*a^2*x^3*(1+a*x)^(1/2)*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^9//2+6//5*a*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^9//2+1//105*a^3*x^4*(1+a*x)^(1/2)*(1+-1*a*x)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*(2718+521*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(-1*arctanh(a*x)), x) == :(-2//5*x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^7//2+-9*a^5//2*x^7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*arcsinh(a^(1/2)*x^(1/2))+2*a*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^7//2+-1//5*a^2*x^3*(1+a*x)^(1/2)*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*(66+7*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(-1*arctanh(a*x)), x) == :(-2//3*x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^5//2+7*a^3//2*x^5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*arcsinh(a^(1/2)*x^(1/2))+1//3*a*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*(18+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(-1*arctanh(a*x)), x) == :(-2*x*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2+a*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2+-5*a^(1/2)*x^3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2*arcsinh(a^(1/2)*x^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-1*x*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+3*a^-1//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(-1*arctanh(a*x)), x) == :(a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-1*a^-3//2*x^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arcsinh(a^(1/2)*x^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(-1*arctanh(a*x)), x) == :(-1*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+-1*a^-5//2*x^-3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arcsinh(a^(1/2)*x^(1/2))+2^(1/2)*a^-5//2*x^-3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(-1*arctanh(a*x)), x) == :((1/2)*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-5//2+3*a^-7//2*x^-5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arcsinh(a^(1/2)*x^(1/2))+3//2*a^-3*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2+-9//4*2^(1/2)*a^-7//2*x^-5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^-7//2*exp(-1*arctanh(a*x)), x) == :(-5*a^-9//2*x^-7//2*(1+-1*a*x)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*arcsinh(a^(1/2)*x^(1/2))+-35//16*a^-4*x^-3*(1+a*x)^(1/2)*(1+-1*a*x)^7//2*(c+-1*c*a^-1*x^-1)^-7//2+-15//16*a^-3*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-7//2+1//4*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-7//2+115//32*2^(1/2)*a^-9//2*x^-7//2*(1+-1*a*x)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^9//2*exp(-2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^9//2+13*a^-1*c^9//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+51*a^-1*c^4*(c+-1*c*a^-1*x^-1)^(1/2)+-5//7*c*a^-1*(c+-1*c*a^-1*x^-1)^7//2+3//5*a^-1*c^2*(c+-1*c*a^-1*x^-1)^5//2+19//3*a^-1*c^3*(c+-1*c*a^-1*x^-1)^3//2+-64*2^(1/2)*a^-1*c^9//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(-2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^7//2+11*a^-1*c^7//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+21*a^-1*c^3*(c+-1*c*a^-1*x^-1)^(1/2)+-3//5*c*a^-1*(c+-1*c*a^-1*x^-1)^5//2+5//3*a^-1*c^2*(c+-1*c*a^-1*x^-1)^3//2+-32*2^(1/2)*a^-1*c^7//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(-2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^5//2+7*a^-1*c^2*(c+-1*c*a^-1*x^-1)^(1/2)+9*a^-1*c^5//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-1//3*c*a^-1*(c+-1*c*a^-1*x^-1)^3//2+-16*2^(1/2)*a^-1*c^5//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(-2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^3//2+c*a^-1*(c+-1*c*a^-1*x^-1)^(1/2)+7*a^-1*c^3//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-8*2^(1/2)*a^-1*c^3//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^(1/2)+5*a^-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-1*(c+-1*c*a^-1*x^-1)^(1/2)+3*a^-1*c^-1//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-2*2^(1/2)*a^-1*c^-1//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(-2*arctanh(a*x)), x) == :(a^-1*c^-3//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-1*x*c^-2*(c+-1*c*a^-1*x^-1)^(1/2)+-1*2^(1/2)*a^-1*c^-3//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-2*(c+-1*c*a^-1*x^-1)^-1//2+-1*a^-1*c^-5//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+2*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-1//2+-1//2*2^(1/2)*a^-1*c^-5//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-7//2*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-2*(c+-1*c*a^-1*x^-1)^-3//2+-3*a^-1*c^-7//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+4//3*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-3//2+7//2*a^-1*c^-3*(c+-1*c*a^-1*x^-1)^-1//2+-1//4*2^(1/2)*a^-1*c^-7//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-9//2*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-2*(c+-1*c*a^-1*x^-1)^-5//2+-5*a^-1*c^-9//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+6//5*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-5//2+11//6*a^-1*c^-3*(c+-1*c*a^-1*x^-1)^-3//2+21//4*a^-1*c^-4*(c+-1*c*a^-1*x^-1)^-1//2+-1//8*2^(1/2)*a^-1*c^-9//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^9//2*exp(-3*arctanh(a*x)), x) == :(-2//7*x*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^9//2+-15*a^7//2*x^9//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*arcsinh(a^(1/2)*x^(1/2))+70*a^3*x^4*(1+a*x)^-1//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^9//2+-50//7*a^2*x^3*(1+a*x)^-1//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^9//2+10//7*a*x^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^9//2+5//7*a^4*x^5*(1+a*x)^-1//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*(587+-109*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(-3*arctanh(a*x)), x) == :(-2//5*x*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^7//2+13*a^5//2*x^7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*arcsinh(a^(1/2)*x^(1/2))+-398//15*a^2*x^3*(1+a*x)^-1//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^7//2+38//15*a*x^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^7//2+-1//15*a^3*x^4*(1+a*x)^-1//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*(2525+-427*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(-3*arctanh(a*x)), x) == :(-2//3*x*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^5//2+-11*a^3//2*x^5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*arcsinh(a^(1/2)*x^(1/2))+26//3*a*x^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^5//2+1//3*a^2*x^3*(1+a*x)^-1//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*(191+-25*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(-3*arctanh(a*x)), x) == :(-2*x*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^3//2+9*a^(1/2)*x^3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2*arcsinh(a^(1/2)*x^(1/2))+-1*a*x^2*(1+a*x)^-1//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-1*x^-1)^3//2*(23+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :(x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+8*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-7*a^-1//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(-3*arctanh(a*x)), x) == :(-1*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-1*x^-1)^-1//2*(1+-1*a*x)+-5*a^-1*(1+a*x)^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+5*a^-3//2*x^-1//2*(1+-1*a*x)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arcsinh(a^(1/2)*x^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(-3*arctanh(a*x)), x) == :(-2*a^-1*(1+a*x)^-1//2*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+-3*a^-5//2*x^-3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arcsinh(a^(1/2)*x^(1/2))+3*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^3//2*(c+-1*c*a^-1*x^-1)^-3//2)
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(-3*arctanh(a*x)), x) == :(a^-2*x^-1*(1+a*x)^-1//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2+a^-7//2*x^-5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arcsinh(a^(1/2)*x^(1/2))+-2*a^-3*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2+(1/2)*2^(1/2)*a^-7//2*x^-5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^-7//2*exp(-3*arctanh(a*x)), x) == :(a^-9//2*x^-7//2*(1+-1*a*x)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*arcsinh(a^(1/2)*x^(1/2))+(1/2)*a^-2*x^-1*(1+a*x)^-1//2*(1+-1*a*x)^5//2*(c+-1*c*a^-1*x^-1)^-7//2+-1//4*a^-3*x^-2*(1+a*x)^-1//2*(1+-1*a*x)^7//2*(c+-1*c*a^-1*x^-1)^-7//2+7//4*a^-4*x^-3*(1+a*x)^(1/2)*(1+-1*a*x)^7//2*(c+-1*c*a^-1*x^-1)^-7//2+-11//8*2^(1/2)*a^-9//2*x^-7//2*(1+-1*a*x)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^-1*exp(3*arctanh(a*x)), x) == :(4*a^2*c^-1*arctanh((1+-1*a^2*x^2)^(1/2))+a*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2)+-8//3*a^2*c^-1*(1+-1*a^2*x^2)^-3//2*(1+a*x)+-4//3*a^2*c^-1*(1+-1*a^2*x^2)^-1//2*(3+4*a*x))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arctanh(a*x)), x) == :(1//3*x^3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-1//8*x*a^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+1//8*a^-5//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+1//12*a^-1*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arctanh(a*x)), x) == :((1/2)*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-1//4*a^-3//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+1//4*x*a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(arctanh(a*x)), x) == :(x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+a^-1//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2)))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arctanh(a*x)), x) == :(-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+2*a^(1/2)*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arctanh(a*x)), x) == :(-2//3*x^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arctanh(a*x)), x) == :(-2//5*x^-2*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+4//15*a*x^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arctanh(a*x)), x) == :(-2//7*x^-3*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-16//105*a^2*x^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+8//35*a*x^-2*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arctanh(a*x)), x) == :(-2//9*x^-4*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-16//105*a^2*x^-2*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+4//21*a*x^-3*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+32//315*a^3*x^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//4*x^4*(c+-1*c*a^-1*x^-1)^(1/2)+-75//64*x*a^-3*(c+-1*c*a^-1*x^-1)^(1/2)+-75//64*a^-4*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-25//32*a^-2*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+-5//8*a^-1*x^3*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//3*x^3*(c+-1*c*a^-1*x^-1)^(1/2)+-11//8*x*a^-2*(c+-1*c*a^-1*x^-1)^(1/2)+-11//8*a^-3*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-11//12*a^-1*x^2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//2*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+-7//4*x*a^-1*(c+-1*c*a^-1*x^-1)^(1/2)+-7//4*a^-2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^(1/2)+-3*a^-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-2*(c+-1*c*a^-1*x^-1)^(1/2)+-2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4*a*(c+-1*c*a^-1*x^-1)^(1/2)+2//3*a*c^-1*(c+-1*c*a^-1*x^-1)^3//2)
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4*a^2*(c+-1*c*a^-1*x^-1)^(1/2)+2*a^2*c^-1*(c+-1*c*a^-1*x^-1)^3//2+-2//5*a^2*c^-2*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4*a^3*(c+-1*c*a^-1*x^-1)^(1/2)+-8//5*a^3*c^-2*(c+-1*c*a^-1*x^-1)^5//2+2//7*a^3*c^-3*(c+-1*c*a^-1*x^-1)^7//2+10//3*a^3*c^-1*(c+-1*c*a^-1*x^-1)^3//2)
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4*a^4*(c+-1*c*a^-1*x^-1)^(1/2)+-18//5*a^4*c^-2*(c+-1*c*a^-1*x^-1)^5//2+-2//9*a^4*c^-4*(c+-1*c*a^-1*x^-1)^9//2+10//7*a^4*c^-3*(c+-1*c*a^-1*x^-1)^7//2+14//3*a^4*c^-1*(c+-1*c*a^-1*x^-1)^3//2)
@test integrate(x^3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-363//64*a^-7//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+-107//64*x*a^-3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-21//32*x*a^-3*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-11//24*a^-2*x^2*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-1//4*a^-1*x^3*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^-7//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-45//8*a^-5//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+-13//8*x*a^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-3//4*x*a^-2*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-1//3*a^-1*x^2*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^-5//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-23//4*a^-3//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+-7//4*x*a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-1//2*x*a^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^-3//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1*x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-5*a^-1//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+4*2^(1/2)*a^-1//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2*a^(1/2)*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+4*2^(1/2)*a^(1/2)*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*a*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//3*x^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^3//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*a^2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//5*x^-2*(1+a*x)^5//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//3*a*x^-1*(1+a*x)^3//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^5//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-104//21*a^3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//7*x^-3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-32//21*a^2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-6//7*a*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^7//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1576//315*a^4*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//9*x^-4*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-472//315*a^3*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-92//105*a^2*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-38//63*a*x^-3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^9//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh(2^(1/2)*a^(1/2)*x^(1/2)*(1+a*x)^-1//2))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-1*x^3*(1+-1*a^2*x^2)^(1/2)*(3+-3*a*x)^-1*(c+-1*c*a^-1*x^-1)^(1/2)+-11//8*x*a^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+11//8*a^-5//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+11//12*a^-1*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-1*x^2*(1+-1*a^2*x^2)^(1/2)*(2+-2*a*x)^-1*(c+-1*c*a^-1*x^-1)^(1/2)+-7//4*a^-3//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+7//4*x*a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-1*x*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+3*a^-1//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2)))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+-2*a^(1/2)*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-2//3*x^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+10//3*a*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-12//5*a^2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//5*x^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+6//5*a*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-2//7*x^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+208//105*a^3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-104//105*a^2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+26//35*a*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//4*x^4*(c+-1*c*a^-1*x^-1)^(1/2)+-363//64*a^-4*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-107//96*a^-2*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+17//24*a^-1*x^3*(c+-1*c*a^-1*x^-1)^(1/2)+149//64*x*a^-3*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^-4*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//3*x^3*(c+-1*c*a^-1*x^-1)^(1/2)+-19//8*x*a^-2*(c+-1*c*a^-1*x^-1)^(1/2)+13//12*a^-1*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+45//8*a^-3*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-3*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//2*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+-23//4*a^-2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+9//4*x*a^-1*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^-2*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-1*x^-1)^(1/2)+5*a^-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-2*(c+-1*c*a^-1*x^-1)^(1/2)+-2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+4*2^(1/2)*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(4*a*(c+-1*c*a^-1*x^-1)^(1/2)+2//3*a*c^-1*(c+-1*c*a^-1*x^-1)^3//2+-4*a*2^(1/2)*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-4*a^2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//3*a^2*c^-1*(c+-1*c*a^-1*x^-1)^3//2+-2//5*a^2*c^-2*(c+-1*c*a^-1*x^-1)^5//2+4*2^(1/2)*a^2*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(4*a^3*(c+-1*c*a^-1*x^-1)^(1/2)+2//3*a^3*c^-1*(c+-1*c*a^-1*x^-1)^3//2+2//7*a^3*c^-3*(c+-1*c*a^-1*x^-1)^7//2+-4*2^(1/2)*a^3*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-4*a^4*(c+-1*c*a^-1*x^-1)^(1/2)+-2//3*a^4*c^-1*(c+-1*c*a^-1*x^-1)^3//2+-2//5*a^4*c^-2*(c+-1*c*a^-1*x^-1)^5//2+-2//9*a^4*c^-4*(c+-1*c*a^-1*x^-1)^9//2+2//7*a^4*c^-3*(c+-1*c*a^-1*x^-1)^7//2+4*2^(1/2)*a^4*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :(8*x^4*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+1//4*x^4*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-1115//64*x*a^-3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-223//24*a^-1*x^3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+1115//64*a^-7//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+1115//96*a^-2*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :(8*x^3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+1//3*x^3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-119//8*a^-5//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2))+-119//12*a^-1*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+119//8*x*a^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :((1/2)*x^2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+8*x^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-47//4*x*a^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+47//4*a^-3//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :(x*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+8*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-7*a^-1//2*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2)))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-10*a*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+2*a^(1/2)*x^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arcsinh(a^(1/2)*x^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-2//3*x^-1*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+20//3*a*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+46//3*x*a^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-316//15*a^2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//5*x^-2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+158//15*a^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+32//15*a*x^-1*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-2//7*x^-3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+2672//105*a^3*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-1336//105*a^2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+44//35*a*x^-2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+334//35*a^2*x^-1*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1312//45*a^4*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//9*x^-4*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-164//15*a^2*x^-2*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+8//9*a*x^-3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+82//9*a^2*x^-2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+656//45*a^3*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(arctanh(a*x)), x) == :(a^-1*c^4*arcsin(a*x)+35//16*a^-1*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//42*a^-8*c^4*x^-7*(1+-1*a^2*x^2)^7//2*(6+7*a*x)+-1//48*a^-4*c^4*x^-3*(1+-1*a^2*x^2)^3//2*(16+35*a*x)+1//16*a^-2*c^4*x^-1*(1+-1*a^2*x^2)^(1/2)*(16+-35*a*x)+1//120*a^-6*c^4*x^-5*(1+-1*a^2*x^2)^5//2*(24+35*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(arctanh(a*x)), x) == :(a^-1*c^3*arcsin(a*x)+15//8*a^-1*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//24*a^-4*c^3*x^-3*(1+-1*a^2*x^2)^3//2*(8+15*a*x)+1//8*a^-2*c^3*x^-1*(1+-1*a^2*x^2)^(1/2)*(8+-15*a*x)+1//20*a^-6*c^3*x^-5*(1+-1*a^2*x^2)^5//2*(4+5*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(arctanh(a*x)), x) == :(a^-1*c^2*arcsin(a*x)+3//2*a^-1*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+(1/2)*a^-2*c^2*x^-1*(1+-1*a^2*x^2)^(1/2)*(2+-3*a*x)+-1//6*a^-4*c^2*x^-3*(1+-1*a^2*x^2)^3//2*(2+3*a*x))
@test integrate((c+-1*c*a^-2*x^-2)*exp(arctanh(a*x)), x) == :(c*a^-1*arcsin(a*x)+c*a^-1*arctanh((1+-1*a^2*x^2)^(1/2))+c*a^-2*x^-1*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(arctanh(a*x)), x) == :(a^-1*c^-1*arcsin(a*x)+-1*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)+-1*a^-1*c^-1*(1+-1*a^2*x^2)^-1//2*(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(arctanh(a*x)), x) == :(a^-1*c^-2*arcsin(a*x)+-8//3*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)+-1//3*x*c^-2*(1+-1*a^2*x^2)^-1//2*(3+4*a*x)+1//3*a^2*c^-2*x^3*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(arctanh(a*x)), x) == :(a^-1*c^-3*arcsin(a*x)+-16//5*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)+-1//5*x*c^-3*(1+-1*a^2*x^2)^-1//2*(5+8*a*x)+-1//5*a^4*c^-3*x^5*(1+-1*a^2*x^2)^-5//2*(1+a*x)+1//15*a^2*c^-3*x^3*(1+-1*a^2*x^2)^-3//2*(5+6*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(arctanh(a*x)), x) == :(a^-1*c^-4*arcsin(a*x)+-128//35*a^-1*c^-4*(1+-1*a^2*x^2)^(1/2)+-1//35*x*c^-4*(1+-1*a^2*x^2)^-1//2*(35+64*a*x)+-1//35*a^4*c^-4*x^5*(1+-1*a^2*x^2)^-5//2*(7+8*a*x)+1//7*a^6*c^-4*x^7*(1+-1*a^2*x^2)^-7//2*(1+a*x)+1//105*a^2*c^-4*x^3*(1+-1*a^2*x^2)^-3//2*(35+48*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^5*exp(2*arctanh(a*x)), x) == :(-1*x*c^5+-4*a^-3*c^5*x^-2+-3*a^-2*c^5*x^-1+-2*a^-1*c^5*log(x)+3*a^-5*c^5*x^-4+-4//3*a^-7*c^5*x^-6+-3//7*a^-8*c^5*x^-7+1//4*a^-9*c^5*x^-8+1//9*a^-10*c^5*x^-9+2//3*a^-4*c^5*x^-3+2//5*a^-6*c^5*x^-5)
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(2*arctanh(a*x)), x) == :(-1*x*c^4+-3*a^-3*c^4*x^-2+-2*a^-1*c^4*log(x)+-2*a^-2*c^4*x^-1+-1//3*a^-7*c^4*x^-6+-1//7*a^-8*c^4*x^-7+2//5*a^-6*c^4*x^-5+3//2*a^-5*c^4*x^-4)
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(2*arctanh(a*x)), x) == :(-1*x*c^3+(1/2)*a^-5*c^3*x^-4+-1*a^-2*c^3*x^-1+-2*a^-1*c^3*log(x)+-2*a^-3*c^3*x^-2+-1//3*a^-4*c^3*x^-3+1//5*a^-6*c^3*x^-5)
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(2*arctanh(a*x)), x) == :(-1*x*c^2+-1*a^-3*c^2*x^-2+-2*a^-1*c^2*log(x)+-1//3*a^-4*c^2*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)*exp(2*arctanh(a*x)), x) == :(-1*c*x+c*a^-2*x^-1+-2*c*a^-1*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(2*arctanh(a*x)), x) == :(-1*x*c^-1+-1*a^-1*c^-1*(1+-1*a*x)^-1+-2*a^-1*c^-1*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(2*arctanh(a*x)), x) == :(-1*x*c^-2+-17//8*a^-1*c^-2*log(1+-1*a*x)+-7//4*a^-1*c^-2*(1+-1*a*x)^-1+1//4*a^-1*c^-2*(1+-1*a*x)^-2+1//8*a^-1*c^-2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(2*arctanh(a*x)), x) == :(-1*x*c^-3+-39//16*a^-1*c^-3*(1+-1*a*x)^-1+-9//4*a^-1*c^-3*log(1+-1*a*x)+-1//12*a^-1*c^-3*(1+-1*a*x)^-3+1//4*a^-1*c^-3*log(1+a*x)+1//16*a^-1*c^-3*(1+a*x)^-1+5//8*a^-1*c^-3*(1+-1*a*x)^-2)
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(2*arctanh(a*x)), x) == :(-1*x*c^-4+-303//128*a^-1*c^-4*log(1+-1*a*x)+-99//32*a^-1*c^-4*(1+-1*a*x)^-1+-13//48*a^-1*c^-4*(1+-1*a*x)^-3+-1//64*a^-1*c^-4*(1+a*x)^-2+1//32*a^-1*c^-4*(1+-1*a*x)^-4+11//64*a^-1*c^-4*(1+a*x)^-1+35//32*a^-1*c^-4*(1+-1*a*x)^-2+47//128*a^-1*c^-4*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(3*arctanh(a*x)), x) == :(-3*a^-1*c^4*arcsin(a*x)+-15//16*a^-1*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*a^-7*c^4*x^-6*(1+-1*a^2*x^2)^7//2+-1//7*a^-8*c^4*x^-7*(1+-1*a^2*x^2)^7//2+-3//16*a^-2*c^4*x^-1*(1+-1*a^2*x^2)^(1/2)*(16+-5*a*x)+-1//40*a^-6*c^4*x^-5*(1+-1*a^2*x^2)^5//2*(24+5*a*x)+1//16*a^-4*c^4*x^-3*(1+-1*a^2*x^2)^3//2*(16+5*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(3*arctanh(a*x)), x) == :(-3*a^-1*c^3*arcsin(a*x)+-3//8*a^-1*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+1//5*a^-6*c^3*x^-5*(1+-1*a^2*x^2)^5//2+3//4*a^-5*c^3*x^-4*(1+-1*a^2*x^2)^5//2+-3//8*a^-2*c^3*x^-1*(1+-1*a^2*x^2)^(1/2)*(8+-1*a*x)+1//8*a^-4*c^3*x^-3*(1+-1*a^2*x^2)^3//2*(8+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(3*arctanh(a*x)), x) == :((1/2)*a^-1*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-3*a^-1*c^2*arcsin(a*x)+-3//2*a^-3*c^2*x^-2*(1+-1*a^2*x^2)^3//2+-1//3*a^-4*c^2*x^-3*(1+-1*a^2*x^2)^3//2+-1//2*a^-2*c^2*x^-1*(1+-1*a^2*x^2)^(1/2)*(6+a*x))
@test integrate((c+-1*c*a^-2*x^-2)*exp(3*arctanh(a*x)), x) == :(c*a^-1*(1+-1*a^2*x^2)^(1/2)+-3*c*a^-1*arcsin(a*x)+3*c*a^-1*arctanh((1+-1*a^2*x^2)^(1/2))+c*a^-2*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(3*arctanh(a*x)), x) == :(-3*a^-1*c^-1*arcsin(a*x)+3*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)+2*a^-1*c^-1*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+-1//3*a^-1*c^-1*(1+a*x)^3*(1+-1*a^2*x^2)^-3//2)
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(3*arctanh(a*x)), x) == :(a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)+-3*a^-1*c^-2*arcsin(a*x)+-6//5*a^-1*c^-2*(1+a*x)^2*(1+-1*a^2*x^2)^-3//2+1//5*a^-1*c^-2*(1+a*x)^3*(1+-1*a^2*x^2)^-5//2+1//5*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(24+24*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(3*arctanh(a*x)), x) == :(a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)+-3*a^-1*c^-3*arcsin(a*x)+-1//7*a^-1*c^-3*(1+a*x)^3*(1+-1*a^2*x^2)^-7//2+-1//35*a^-1*c^-3*(1+-1*a^2*x^2)^-3//2*(137+137*a*x)+1//35*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(245+181*a*x)+38//35*a^-1*c^-3*(1+a*x)^2*(1+-1*a^2*x^2)^-5//2)
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(3*arctanh(a*x)), x) == :(a^-1*c^-4*(1+-1*a^2*x^2)^(1/2)+-3*a^-1*c^-4*arcsin(a*x)+-22//21*a^-1*c^-4*(1+a*x)^2*(1+-1*a^2*x^2)^-7//2+-1//315*a^-1*c^-4*(1+-1*a^2*x^2)^-3//2*(2310+1658*a*x)+1//9*a^-1*c^-4*(1+a*x)^3*(1+-1*a^2*x^2)^-9//2+1//105*a^-1*c^-4*(1+-1*a^2*x^2)^-5//2*(478+478*a*x)+1//315*a^-1*c^-4*(1+-1*a^2*x^2)^-1//2*(2520+1724*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^5*exp(4*arctanh(a*x)), x) == :(x*c^5+(1/2)*a^-9*c^5*x^-8+-3*a^-2*c^5*x^-1+4*a^-1*c^5*log(x)+4*a^-3*c^5*x^-2+-14//5*a^-6*c^5*x^-5+-4//3*a^-7*c^5*x^-6+1//9*a^-10*c^5*x^-9+3//7*a^-8*c^5*x^-7+14//3*a^-4*c^5*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(4*arctanh(a*x)), x) == :(x*c^4+a^-5*c^4*x^-4+-4*a^-2*c^4*x^-1+2*a^-3*c^4*x^-2+4*a^-1*c^4*log(x)+-4//5*a^-6*c^4*x^-5+-2//3*a^-7*c^4*x^-6+-1//7*a^-8*c^4*x^-7+10//3*a^-4*c^4*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(4*arctanh(a*x)), x) == :(x*c^3+a^-5*c^3*x^-4+-5*a^-2*c^3*x^-1+4*a^-1*c^3*log(x)+1//5*a^-6*c^3*x^-5+5//3*a^-4*c^3*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(4*arctanh(a*x)), x) == :(x*c^2+-6*a^-2*c^2*x^-1+-2*a^-3*c^2*x^-2+4*a^-1*c^2*log(x)+-1//3*a^-4*c^2*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)*exp(4*arctanh(a*x)), x) == :(c*x+c*a^-2*x^-1+-4*c*a^-1*log(x)+8*c*a^-1*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(4*arctanh(a*x)), x) == :(x*c^-1+-1*a^-1*c^-1*(1+-1*a*x)^-2+4*a^-1*c^-1*log(1+-1*a*x)+5*a^-1*c^-1*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(4*arctanh(a*x)), x) == :(x*c^-2+-2*a^-1*c^-2*(1+-1*a*x)^-2+4*a^-1*c^-2*log(1+-1*a*x)+6*a^-1*c^-2*(1+-1*a*x)^-1+1//3*a^-1*c^-2*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(4*arctanh(a*x)), x) == :(x*c^-3+-49//16*a^-1*c^-3*(1+-1*a*x)^-2+-1//8*a^-1*c^-3*(1+-1*a*x)^-4+-1//32*a^-1*c^-3*log(1+a*x)+11//12*a^-1*c^-3*(1+-1*a*x)^-3+111//16*a^-1*c^-3*(1+-1*a*x)^-1+129//32*a^-1*c^-3*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(4*arctanh(a*x)), x) == :(x*c^-4+-67//16*a^-1*c^-4*(1+-1*a*x)^-2+-7//16*a^-1*c^-4*(1+-1*a*x)^-4+-5//64*a^-1*c^-4*log(1+a*x)+-1//64*a^-1*c^-4*(1+a*x)^-1+1//20*a^-1*c^-4*(1+-1*a*x)^-5+83//48*a^-1*c^-4*(1+-1*a*x)^-3+261//64*a^-1*c^-4*log(1+-1*a*x)+501//64*a^-1*c^-4*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(-1*arctanh(a*x)), x) == :(a^-1*c^4*arcsin(a*x)+-35//16*a^-1*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//42*a^-8*c^4*x^-7*(1+-1*a^2*x^2)^7//2*(6+-7*a*x)+-1//48*a^-4*c^4*x^-3*(1+-1*a^2*x^2)^3//2*(16+-35*a*x)+1//16*a^-2*c^4*x^-1*(1+-1*a^2*x^2)^(1/2)*(16+35*a*x)+1//120*a^-6*c^4*x^-5*(1+-1*a^2*x^2)^5//2*(24+-35*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(-1*arctanh(a*x)), x) == :(a^-1*c^3*arcsin(a*x)+-15//8*a^-1*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//24*a^-4*c^3*x^-3*(1+-1*a^2*x^2)^3//2*(8+-15*a*x)+1//8*a^-2*c^3*x^-1*(1+-1*a^2*x^2)^(1/2)*(8+15*a*x)+1//20*a^-6*c^3*x^-5*(1+-1*a^2*x^2)^5//2*(4+-5*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(-1*arctanh(a*x)), x) == :(a^-1*c^2*arcsin(a*x)+-3//2*a^-1*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+(1/2)*a^-2*c^2*x^-1*(1+-1*a^2*x^2)^(1/2)*(2+3*a*x)+-1//6*a^-4*c^2*x^-3*(1+-1*a^2*x^2)^3//2*(2+-3*a*x))
@test integrate((c+-1*c*a^-2*x^-2)*exp(-1*arctanh(a*x)), x) == :(c*a^-1*arcsin(a*x)+-1*c*a^-1*arctanh((1+-1*a^2*x^2)^(1/2))+c*a^-2*x^-1*(1+-1*a^2*x^2)^(1/2)*(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)+a^-1*c^-1*arcsin(a*x)+a^-1*c^-1*(1+-1*a^2*x^2)^-1//2*(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-2*arcsin(a*x)+8//3*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)+-1//3*x*c^-2*(1+-1*a^2*x^2)^-1//2*(3+-4*a*x)+1//3*a^2*c^-2*x^3*(1+-1*a^2*x^2)^-3//2*(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-3*arcsin(a*x)+16//5*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)+-1//5*x*c^-3*(1+-1*a^2*x^2)^-1//2*(5+-8*a*x)+-1//5*a^4*c^-3*x^5*(1+-1*a^2*x^2)^-5//2*(1+-1*a*x)+1//15*a^2*c^-3*x^3*(1+-1*a^2*x^2)^-3//2*(5+-6*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(-1*arctanh(a*x)), x) == :(a^-1*c^-4*arcsin(a*x)+128//35*a^-1*c^-4*(1+-1*a^2*x^2)^(1/2)+-1//35*x*c^-4*(1+-1*a^2*x^2)^-1//2*(35+-64*a*x)+-1//35*a^4*c^-4*x^5*(1+-1*a^2*x^2)^-5//2*(7+-8*a*x)+1//7*a^6*c^-4*x^7*(1+-1*a^2*x^2)^-7//2*(1+-1*a*x)+1//105*a^2*c^-4*x^3*(1+-1*a^2*x^2)^-3//2*(35+-48*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(-2*arctanh(a*x)), x) == :(-1*x*c^4+-2*a^-2*c^4*x^-1+2*a^-1*c^4*log(x)+3*a^-3*c^4*x^-2+-3//2*a^-5*c^4*x^-4+-1//7*a^-8*c^4*x^-7+1//3*a^-7*c^4*x^-6+2//5*a^-6*c^4*x^-5)
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(-2*arctanh(a*x)), x) == :(-1*x*c^3+-1*a^-2*c^3*x^-1+2*a^-1*c^3*log(x)+2*a^-3*c^3*x^-2+-1//2*a^-5*c^3*x^-4+-1//3*a^-4*c^3*x^-3+1//5*a^-6*c^3*x^-5)
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(-2*arctanh(a*x)), x) == :(-1*x*c^2+a^-3*c^2*x^-2+2*a^-1*c^2*log(x)+-1//3*a^-4*c^2*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)*exp(-2*arctanh(a*x)), x) == :(-1*c*x+c*a^-2*x^-1+2*c*a^-1*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-1+a^-1*c^-1*(1+a*x)^-1+2*a^-1*c^-1*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-2+-1//4*a^-1*c^-2*(1+a*x)^-2+-1//8*a^-1*c^-2*log(1+-1*a*x)+7//4*a^-1*c^-2*(1+a*x)^-1+17//8*a^-1*c^-2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-3+-5//8*a^-1*c^-3*(1+a*x)^-2+-1//4*a^-1*c^-3*log(1+-1*a*x)+-1//16*a^-1*c^-3*(1+-1*a*x)^-1+1//12*a^-1*c^-3*(1+a*x)^-3+9//4*a^-1*c^-3*log(1+a*x)+39//16*a^-1*c^-3*(1+a*x)^-1)
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(-2*arctanh(a*x)), x) == :(-1*x*c^-4+-47//128*a^-1*c^-4*log(1+-1*a*x)+-35//32*a^-1*c^-4*(1+a*x)^-2+-11//64*a^-1*c^-4*(1+-1*a*x)^-1+-1//32*a^-1*c^-4*(1+a*x)^-4+1//64*a^-1*c^-4*(1+-1*a*x)^-2+13//48*a^-1*c^-4*(1+a*x)^-3+99//32*a^-1*c^-4*(1+a*x)^-1+303//128*a^-1*c^-4*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(-3*arctanh(a*x)), x) == :(-3*a^-1*c^4*arcsin(a*x)+15//16*a^-1*c^4*arctanh((1+-1*a^2*x^2)^(1/2))+(1/2)*a^-7*c^4*x^-6*(1+-1*a^2*x^2)^7//2+-1//7*a^-8*c^4*x^-7*(1+-1*a^2*x^2)^7//2+-3//16*a^-2*c^4*x^-1*(1+-1*a^2*x^2)^(1/2)*(16+5*a*x)+-1//40*a^-6*c^4*x^-5*(1+-1*a^2*x^2)^5//2*(24+-5*a*x)+1//16*a^-4*c^4*x^-3*(1+-1*a^2*x^2)^3//2*(16+-5*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(-3*arctanh(a*x)), x) == :(-3*a^-1*c^3*arcsin(a*x)+3//8*a^-1*c^3*arctanh((1+-1*a^2*x^2)^(1/2))+-3//4*a^-5*c^3*x^-4*(1+-1*a^2*x^2)^5//2+1//5*a^-6*c^3*x^-5*(1+-1*a^2*x^2)^5//2+-3//8*a^-2*c^3*x^-1*(1+-1*a^2*x^2)^(1/2)*(8+a*x)+1//8*a^-4*c^3*x^-3*(1+-1*a^2*x^2)^3//2*(8+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(-3*arctanh(a*x)), x) == :(-3*a^-1*c^2*arcsin(a*x)+-1//2*a^-1*c^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*a^-4*c^2*x^-3*(1+-1*a^2*x^2)^3//2+3//2*a^-3*c^2*x^-2*(1+-1*a^2*x^2)^3//2+-1//2*a^-2*c^2*x^-1*(1+-1*a^2*x^2)^(1/2)*(6+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)*exp(-3*arctanh(a*x)), x) == :(-1*c*a^-1*(1+-1*a^2*x^2)^(1/2)+-3*c*a^-1*arcsin(a*x)+-3*c*a^-1*arctanh((1+-1*a^2*x^2)^(1/2))+c*a^-2*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(-3*arctanh(a*x)), x) == :(-3*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)+-3*a^-1*c^-1*arcsin(a*x)+-2*a^-1*c^-1*(1+-1*a*x)^2*(1+-1*a^2*x^2)^-1//2+1//3*a^-1*c^-1*(1+-1*a*x)^3*(1+-1*a^2*x^2)^-3//2)
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)+-3*a^-1*c^-2*arcsin(a*x)+-1//5*a^-1*c^-2*(1+-1*a*x)^3*(1+-1*a^2*x^2)^-5//2+-1//5*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(24+-24*a*x)+6//5*a^-1*c^-2*(1+-1*a*x)^2*(1+-1*a^2*x^2)^-3//2)
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)+-3*a^-1*c^-3*arcsin(a*x)+-38//35*a^-1*c^-3*(1+-1*a*x)^2*(1+-1*a^2*x^2)^-5//2+-1//35*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(245+-181*a*x)+1//7*a^-1*c^-3*(1+-1*a*x)^3*(1+-1*a^2*x^2)^-7//2+1//35*a^-1*c^-3*(1+-1*a^2*x^2)^-3//2*(137+-137*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*c^-4*(1+-1*a^2*x^2)^(1/2)+-3*a^-1*c^-4*arcsin(a*x)+-1//9*a^-1*c^-4*(1+-1*a*x)^3*(1+-1*a^2*x^2)^-9//2+-1//105*a^-1*c^-4*(1+-1*a^2*x^2)^-5//2*(478+-478*a*x)+-1//315*a^-1*c^-4*(1+-1*a^2*x^2)^-1//2*(2520+-1724*a*x)+1//315*a^-1*c^-4*(1+-1*a^2*x^2)^-3//2*(2310+-1658*a*x)+22//21*a^-1*c^-4*(1+-1*a*x)^2*(1+-1*a^2*x^2)^-7//2)
@test integrate((c+-1*c*a^-2*x^-2)^9//2*exp(arctanh(a*x)), x) == :(-1//8*x*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+a^9*x^10*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-2*a^5*x^6*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+2*a^6*x^7*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+4*a^7*x^8*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-3//2*a^4*x^5*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-1//7*a*x^2*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+2//3*a^2*x^3*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+4//5*a^3*x^4*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+a^8*x^9*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(arctanh(a*x)), x) == :(-1//6*x*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+a^3*x^4*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-1*a^7*x^8*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-3*a^5*x^6*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-3//2*a^4*x^5*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-1//5*a*x^2*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+3//4*a^2*x^3*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-1*a^6*x^7*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(arctanh(a*x)), x) == :(-1//4*x*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+a^2*x^3*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+a^5*x^6*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+2*a^3*x^4*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-1//3*a*x^2*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+a^4*x^5*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(arctanh(a*x)), x) == :(-1//2*x*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+-1*a*x^2*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+-1*a^3*x^4*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+-1*a^2*x^3*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(arctanh(a*x)), x) == :(a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(arctanh(a*x)), x) == :(-1*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1*a^-2*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(arctanh(a*x)), x) == :(a^-3*x^-2*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+(1/2)*a^-4*x^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+-1//4*a^-4*x^-3*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*log(1+a*x)+5//4*a^-4*x^-3*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(arctanh(a*x)), x) == :(-1*a^-5*x^-4*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+-1*a^-6*x^-5*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+-23//16*a^-6*x^-5*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*log(1+-1*a*x)+1//8*a^-6*x^-5*(1+a*x)^-1*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+1//8*a^-6*x^-5*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+7//16*a^-6*x^-5*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(arctanh(a*x)), x) == :(a^-7*x^-6*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+-19//32*a^-8*x^-7*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*log(1+a*x)+-11//32*a^-8*x^-7*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+-5//16*a^-8*x^-7*(1+a*x)^-1*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+1//24*a^-8*x^-7*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+1//32*a^-8*x^-7*(1+a*x)^-2*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+3//2*a^-8*x^-7*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+51//32*a^-8*x^-7*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^9//2*exp(2*arctanh(a*x)), x) == :(-1*x*(8+-8*a*x)^-1*(c+-1*c*a^-2*x^-2)^9//2*(1+a*x)+295//1344*a^4*x^5*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2+-501//128*a^8*x^9*(1+a*x)^-4*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2+-127//420*a^3*x^4*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2*(1+a*x)+-1//28*a*x^2*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^9//2*(1+a*x)+71//336*a^2*x^3*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^9//2*(1+a*x)+373//192*a^7*x^8*(1+a*x)^-3*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2+501//640*a^6*x^7*(1+a*x)^-2*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2+661//1680*a^5*x^6*(1+a*x)^-1*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2+2*a^8*x^9*(1+a*x)^-9//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-2*x^-2)^9//2*arcsin(a*x)+245//128*a^8*x^9*(1+a*x)^-9//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-2*x^-2)^9//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(2*arctanh(a*x)), x) == :(-1*x*(6+-6*a*x)^-1*(c+-1*c*a^-2*x^-2)^7//2*(1+a*x)+-11//30*a^3*x^4*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+-57//80*a^4*x^5*(1+a*x)^-1*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+-41//24*a^5*x^6*(1+a*x)^-2*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+-1//15*a*x^2*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^7//2*(1+a*x)+13//40*a^2*x^3*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2*(1+a*x)+57//16*a^6*x^7*(1+a*x)^-3*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+-2*a^6*x^7*(1+a*x)^-7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*arcsin(a*x)+-25//16*a^6*x^7*(1+a*x)^-7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(2*arctanh(a*x)), x) == :(-1*x*(4+-4*a*x)^-1*(c+-1*c*a^-2*x^-2)^5//2*(1+a*x)+5//8*a^2*x^3*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+-25//8*a^4*x^5*(1+a*x)^-2*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+-1//6*a*x^2*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2*(1+a*x)+17//12*a^3*x^4*(1+a*x)^-1*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+2*a^4*x^5*(1+a*x)^-5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*arcsin(a*x)+9//8*a^4*x^5*(1+a*x)^-5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(2*arctanh(a*x)), x) == :(-1*a*x^2*(1+-1*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2+-1*x*(2+-2*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2*(1+a*x)+5*a^2*x^3*(1+a*x)^-1*(2+-2*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2+-2*a^2*x^3*(1+a*x)^-3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*arcsin(a*x)+-1//2*a^2*x^3*(1+a*x)^-3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-2*x^-2)^(1/2)+-1*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+2*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(2*arctanh(a*x)), x) == :(a^-2*x^-1*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-1//2+a^-2*x^-1*(c+-1*c*a^-2*x^-2)^-1//2*(1+a*x)*(2+-2*a*x)+-2*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(2*arctanh(a*x)), x) == :(1//3*a^-2*x^-1*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-3//2+2*a^-4*x^-3*(1+a*x)^3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*arcsin(a*x)+-1//3*a^-4*x^-3*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-3//2*(1+-1*a*x)*(10+-4*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(2*arctanh(a*x)), x) == :(1//5*a^-2*x^-1*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-5//2+-1//3*a^-3*x^-2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-5//2*(2+-2*a*x)+58//15*a^-4*x^-3*(1+a*x)^2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-5//2+-2*a^-6*x^-5*(1+a*x)^5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*arcsin(a*x)+2//15*a^-6*x^-5*(1+a*x)^2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-5//2*(28+43*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(2*arctanh(a*x)), x) == :(1//7*a^-2*x^-1*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-7//2+-782//105*a^-5*x^-4*(1+a*x)^2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-7//2+-142//35*a^-6*x^-5*(1+a*x)^2*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2+-1//5*a^-3*x^-2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-7//2*(2+-2*a*x)+124//105*a^-4*x^-3*(1+a*x)^2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-7//2+2*a^-8*x^-7*(1+a*x)^7//2*(1+-1*a*x)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*arcsin(a*x)+-2//35*a^-8*x^-7*(1+a*x)^3*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2*(72+107*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-9//2*exp(2*arctanh(a*x)), x) == :(1//9*a^-2*x^-1*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-9//2+-646//315*a^-5*x^-4*(1+a*x)^2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-9//2+-1//7*a^-3*x^-2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-9//2*(2+-2*a*x)+214//315*a^-4*x^-3*(1+a*x)^2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-9//2+302//21*a^-6*x^-5*(1+a*x)^2*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-9//2+1334//315*a^-8*x^-7*(1+a*x)^3*(1+-1*a*x)^5*(c+-1*c*a^-2*x^-2)^-9//2+2458//315*a^-7*x^-6*(1+a*x)^2*(1+-1*a*x)^5*(c+-1*c*a^-2*x^-2)^-9//2+-2*a^-10*x^-9*(1+a*x)^9//2*(1+-1*a*x)^9//2*(c+-1*c*a^-2*x^-2)^-9//2*arcsin(a*x)+2//315*a^-10*x^-9*(1+a*x)^4*(1+-1*a*x)^5*(c+-1*c*a^-2*x^-2)^-9//2*(704+1019*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^9//2*exp(3*arctanh(a*x)), x) == :(-1//8*x*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-1*a^9*x^10*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-4*a^6*x^7*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-2*a^5*x^6*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-3//7*a*x^2*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+3//2*a^4*x^5*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+8//5*a^3*x^4*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-3*a^8*x^9*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(3*arctanh(a*x)), x) == :(-1//6*x*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+a^7*x^8*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-1*a^5*x^6*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-3//5*a*x^2*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-1//4*a^2*x^3*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+5//2*a^4*x^5*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+5//3*a^3*x^4*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+3*a^6*x^7*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(3*arctanh(a*x)), x) == :(-1//4*x*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-1*a*x^2*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-1*a^2*x^3*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-1*a^5*x^6*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+2*a^3*x^4*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-3*a^4*x^5*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(3*arctanh(a*x)), x) == :(-1//2*x*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+a^3*x^4*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+-3*a*x^2*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+3*a^2*x^3*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(3*arctanh(a*x)), x) == :(a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+2*a^-2*x^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+3*a^-2*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(3*arctanh(a*x)), x) == :(-1*a^-3*x^-2*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+(1/2)*a^-4*x^-3*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+-3*a^-4*x^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+-3*a^-4*x^-3*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(3*arctanh(a*x)), x) == :(a^-5*x^-4*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+-9//8*a^-6*x^-5*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+-1//16*a^-6*x^-5*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*log(1+a*x)+1//6*a^-6*x^-5*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+31//8*a^-6*x^-5*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+49//16*a^-6*x^-5*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(3*arctanh(a*x)), x) == :(-1*a^-7*x^-6*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+-201//64*a^-8*x^-7*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*log(1+-1*a*x)+-75//16*a^-8*x^-7*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+-1//2*a^-8*x^-7*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+1//16*a^-8*x^-7*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+1//32*a^-8*x^-7*(1+a*x)^-1*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+9//64*a^-8*x^-7*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*log(1+a*x)+59//32*a^-8*x^-7*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2)
@test integrate((c+-1*c*a^-2*x^-2)^9//2*exp(-1*arctanh(a*x)), x) == :(-1//8*x*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-1*a^9*x^10*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-4*a^7*x^8*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+2*a^5*x^6*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+2*a^6*x^7*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-4//5*a^3*x^4*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-3//2*a^4*x^5*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+1//7*a*x^2*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+2//3*a^2*x^3*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+a^8*x^9*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(-1*arctanh(a*x)), x) == :(-1//6*x*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+a^7*x^8*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-1*a^3*x^4*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+3*a^5*x^6*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-3//2*a^4*x^5*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+1//5*a*x^2*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+3//4*a^2*x^3*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-1*a^6*x^7*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(-1*arctanh(a*x)), x) == :(-1//4*x*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+a^2*x^3*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-1*a^5*x^6*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-2*a^3*x^4*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+1//3*a*x^2*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+a^4*x^5*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(-1*arctanh(a*x)), x) == :(-1//2*x*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+a*x^2*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+a^3*x^4*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+-1*a^2*x^3*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(-1*arctanh(a*x)), x) == :(a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1*a^-2*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(-1*arctanh(a*x)), x) == :(-1*a^-3*x^-2*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+(1/2)*a^-4*x^-3*(1+a*x)^-1*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+-1//4*a^-4*x^-3*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*log(1+-1*a*x)+5//4*a^-4*x^-3*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(-1*arctanh(a*x)), x) == :(a^-5*x^-4*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+-1*a^-6*x^-5*(1+a*x)^-1*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+-23//16*a^-6*x^-5*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*log(1+a*x)+1//8*a^-6*x^-5*(1+a*x)^-2*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+1//8*a^-6*x^-5*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+7//16*a^-6*x^-5*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(-1*arctanh(a*x)), x) == :(-1*a^-7*x^-6*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+-19//32*a^-8*x^-7*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*log(1+-1*a*x)+-11//32*a^-8*x^-7*(1+a*x)^-2*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+-5//16*a^-8*x^-7*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+1//24*a^-8*x^-7*(1+a*x)^-3*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+1//32*a^-8*x^-7*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+3//2*a^-8*x^-7*(1+a*x)^-1*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+51//32*a^-8*x^-7*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^9//2*exp(-2*arctanh(a*x)), x) == :(a*x^2*(28+28*a*x)^-1*(c+-1*c*a^-2*x^-2)^9//2+-1*x*(8+8*a*x)^-1*(c+-1*c*a^-2*x^-2)^9//2*(1+-1*a*x)+47*a^2*x^3*(1+a*x)^-1*(336+-336*a*x)^-1*(c+-1*c*a^-2*x^-2)^9//2+-103//160*a^5*x^6*(1+a*x)^-1*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2+-11//640*a^6*x^7*(1+a*x)^-2*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2+-2//5*a^3*x^4*(1+a*x)^-1*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^9//2+11//128*a^8*x^9*(1+a*x)^-4*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2+39//64*a^7*x^8*(1+a*x)^-3*(1+-1*a*x)^-4*(c+-1*c*a^-2*x^-2)^9//2+629//960*a^4*x^5*(1+a*x)^-1*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^9//2+-2*a^8*x^9*(1+a*x)^-9//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-2*x^-2)^9//2*arcsin(a*x)+245//128*a^8*x^9*(1+a*x)^-9//2*(1+-1*a*x)^-9//2*(c+-1*c*a^-2*x^-2)^9//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(-2*arctanh(a*x)), x) == :(a*x^2*(15+15*a*x)^-1*(c+-1*c*a^-2*x^-2)^7//2+-1*x*(6+6*a*x)^-1*(c+-1*c*a^-2*x^-2)^7//2*(1+-1*a*x)+23*a^2*x^3*(1+a*x)^-1*(120+-120*a*x)^-1*(c+-1*c*a^-2*x^-2)^7//2+-7//16*a^6*x^7*(1+a*x)^-3*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+-3//8*a^5*x^6*(1+a*x)^-2*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+-2//3*a^3*x^4*(1+a*x)^-1*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^7//2+19//16*a^4*x^5*(1+a*x)^-1*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+2*a^6*x^7*(1+a*x)^-7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*arcsin(a*x)+-25//16*a^6*x^7*(1+a*x)^-7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(-2*arctanh(a*x)), x) == :(a*x^2*(6+6*a*x)^-1*(c+-1*c*a^-2*x^-2)^5//2+-1*x*(4+4*a*x)^-1*(c+-1*c*a^-2*x^-2)^5//2*(1+-1*a*x)+-2*a^3*x^4*(1+a*x)^-1*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+7*a^2*x^3*(1+a*x)^-1*(24+-24*a*x)^-1*(c+-1*c*a^-2*x^-2)^5//2+7//8*a^4*x^5*(1+a*x)^-2*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+-2*a^4*x^5*(1+a*x)^-5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*arcsin(a*x)+9//8*a^4*x^5*(1+a*x)^-5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(-2*arctanh(a*x)), x) == :(a*x^2*(1+a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2+-1*x*(2+2*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2*(1+-1*a*x)+5*a^2*x^3*(1+a*x)^-1*(2+-2*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2+2*a^2*x^3*(1+a*x)^-3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*arcsin(a*x)+-1//2*a^2*x^3*(1+a*x)^-3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-2*x^-2)^(1/2)+-1*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+-2*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(-2*arctanh(a*x)), x) == :(a^-2*x^-1*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-1//2+a^-2*x^-1*(c+-1*c*a^-2*x^-2)^-1//2*(1+a*x)*(2+-2*a*x)+2*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(-2*arctanh(a*x)), x) == :(1//3*a^-2*x^-1*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-3//2+-2*a^-4*x^-3*(1+a*x)^3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*arcsin(a*x)+-2//3*a^-4*x^-3*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-3//2*(1+a*x)*(5+2*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(-2*arctanh(a*x)), x) == :(a^-2*x^-1*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-5//2+2//5*a^-3*x^-2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-5//2+-2//15*a^-4*x^-3*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-5//2*(1+a*x)+2*a^-6*x^-5*(1+a*x)^5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*arcsin(a*x)+2//15*a^-6*x^-5*(1+a*x)^2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-5//2*(28+13*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(-2*arctanh(a*x)), x) == :(-12//7*a^-4*x^-3*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2+-10//3*a^-3*x^-2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-7//2+1//3*a^-2*x^-1*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-7//2+-82//105*a^-5*x^-4*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2*(1+a*x)+-2//35*a^-6*x^-5*(1+a*x)^2*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2+-2*a^-8*x^-7*(1+a*x)^7//2*(1+-1*a*x)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*arcsin(a*x)+-2//35*a^-8*x^-7*(1+a*x)^3*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2*(72+37*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^9//2*exp(-3*arctanh(a*x)), x) == :(-1//8*x*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+a^9*x^10*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-4*a^6*x^7*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+2*a^5*x^6*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-8//5*a^3*x^4*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+3//2*a^4*x^5*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+3//7*a*x^2*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2+-3*a^8*x^9*(1+-1*a^2*x^2)^-9//2*(c+-1*c*a^-2*x^-2)^9//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(-3*arctanh(a*x)), x) == :(-1//6*x*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+a^5*x^6*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-1*a^7*x^8*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-5//3*a^3*x^4*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+-1//4*a^2*x^3*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+3//5*a*x^2*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+5//2*a^4*x^5*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2+3*a^6*x^7*(1+-1*a^2*x^2)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(-3*arctanh(a*x)), x) == :(-1//4*x*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+a*x^2*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+a^5*x^6*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-1*a^2*x^3*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-2*a^3*x^4*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2+-3*a^4*x^5*(1+-1*a^2*x^2)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(-3*arctanh(a*x)), x) == :(-1//2*x*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+-1*a^3*x^4*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+3*a*x^2*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2+3*a^2*x^3*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-4*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+2*a^-2*x^-1*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+3*a^-2*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(-3*arctanh(a*x)), x) == :(a^-3*x^-2*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+(1/2)*a^-4*x^-3*(1+a*x)^-2*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+-3*a^-4*x^-3*(1+a*x)^-1*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2+-3*a^-4*x^-3*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(-3*arctanh(a*x)), x) == :(-1*a^-5*x^-4*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+-9//8*a^-6*x^-5*(1+a*x)^-2*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+-1//16*a^-6*x^-5*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*log(1+-1*a*x)+1//6*a^-6*x^-5*(1+a*x)^-3*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+31//8*a^-6*x^-5*(1+a*x)^-1*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2+49//16*a^-6*x^-5*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(-3*arctanh(a*x)), x) == :(a^-7*x^-6*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+-201//64*a^-8*x^-7*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*log(1+a*x)+-75//16*a^-8*x^-7*(1+a*x)^-1*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+-1//2*a^-8*x^-7*(1+a*x)^-3*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+1//16*a^-8*x^-7*(1+a*x)^-4*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+1//32*a^-8*x^-7*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2+9//64*a^-8*x^-7*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*log(1+-1*a*x)+59//32*a^-8*x^-7*(1+a*x)^-2*(1+-1*a^2*x^2)^7//2*(c+-1*c*a^-2*x^-2)^-7//2)
@test integrate(x^m*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arctanh(a*x)), x) == :(m^-1*x^(1+m)*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a*x^(2+m)*(1+m)^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arctanh(a*x)), x) == :((1/2)*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*a*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arctanh(a*x)), x) == :(x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*a*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(arctanh(a*x)), x) == :(a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arctanh(a*x)), x) == :(-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arctanh(a*x)), x) == :(-1//2*x^-1*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-7//8*x*a^-3*(c+-1*c*a^-2*x^-2)^(1/2)+-7//24*x*a^-3*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+-1//4*a^-2*x^2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//6*x*a^-3*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+7//8*x*a^-3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*x*a^-2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*x*a^-2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*x*a^-2*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+x*a^-2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-3//2*x*a^-1*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*x*a^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+3//2*x*a^-1*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-2*x^-2)^(1/2)+-1*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+2*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*(c+-1*c*a^-2*x^-2)^(1/2)+a*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x)+-2*a*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-3//2*a*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+-3//2*x*a^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*a^2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*x^-2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*a*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+-1*x*a^3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-4//3*a^3*(c+-1*c*a^-2*x^-2)^(1/2)+-1//4*x^-3*(c+-1*c*a^-2*x^-2)^(1/2)+-7//8*a^2*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)+-2//3*a*x^-2*(c+-1*c*a^-2*x^-2)^(1/2)+-7//8*x*a^4*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-5*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-6//5*a^4*(c+-1*c*a^-2*x^-2)^(1/2)+-1//5*x^-4*(c+-1*c*a^-2*x^-2)^(1/2)+-3//4*a^3*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)+-3//5*a^2*x^-2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*a*x^-3*(c+-1*c*a^-2*x^-2)^(1/2)+-3//4*x*a^5*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^-2*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-2*a^-1*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//4*a*x^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-3//2*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^-1*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*a*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-3*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*a*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+3*a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-3*a*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+4*x*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3//2*a*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+4*x*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-4*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//4*x^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-2*a^2*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+4*x*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-5*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-4*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//5*x^-4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-2*a^3*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4//3*a^2*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3//4*a*x^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+4*x*a^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^m*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(m^-1*x^(1+m)*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a*x^(2+m)*(1+m)^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arctanh(a*x)), x) == :((1/2)*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*a*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*a*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-1//2*x^-1*(1+-1*a*x)^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(7//8*x*a^-3*(c+-1*c*a^-2*x^-2)^(1/2)+-1//4*a^-2*x^2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+1//6*x*a^-3*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+7//24*x*a^-3*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+7//8*x*a^-3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*x*a^-2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*x*a^-2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*x*a^-2*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+-1*x*a^-2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(3//2*x*a^-1*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*x*a^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+3//2*x*a^-1*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*x*(c+-1*c*a^-2*x^-2)^(1/2)+-1*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+-2*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*(c+-1*c*a^-2*x^-2)^(1/2)+a*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x)+2*a*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(3//2*a*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+-3//2*x*a^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*a^2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*x^-2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*a*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+x*a^3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//4*x^-3*(c+-1*c*a^-2*x^-2)^(1/2)+4//3*a^3*(c+-1*c*a^-2*x^-2)^(1/2)+-7//8*a^2*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)+2//3*a*x^-2*(c+-1*c*a^-2*x^-2)^(1/2)+-7//8*x*a^4*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-5*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-6//5*a^4*(c+-1*c*a^-2*x^-2)^(1/2)+-1//5*x^-4*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*a*x^-3*(c+-1*c*a^-2*x^-2)^(1/2)+-3//5*a^2*x^-2*(c+-1*c*a^-2*x^-2)^(1/2)+3//4*a^3*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)+3//4*x*a^5*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^-2*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+2*a^-1*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//4*a*x^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*x*a^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-3//2*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^-1*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*a*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-3*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*a*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*x*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-4*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3*a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(3*a*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x)+4*x*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-4*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3//2*a*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*x*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate(x^-4*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(4*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//4*x^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-2*a^2*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x)+4*x*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-5*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-4*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//5*x^-4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+2*a^3*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4//3*a^2*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3//4*a*x^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*x*a^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate(x*(1+x)^(1/2)*exp(arctanh(x))*sin(x), x) == :(-1*(1+-1x)^3//2*cos(x)+3*(1+-1x)^(1/2)*cos(x)+-3//2*(1+-1x)^(1/2)*sin(x)+-5//4*2^(1/2)*pi^(1/2)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1)+-3//2*2^(1/2)*pi^(1/2)*cos(1)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))+-3//2*2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1)+5//4*2^(1/2)*pi^(1/2)*cos(1)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2)))
@test integrate((1+x)^(1/2)*exp(arctanh(x))*sin(x), x) == :((1+-1x)^(1/2)*cos(x)+-2*2^(1/2)*pi^(1/2)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1)+2*2^(1/2)*pi^(1/2)*cos(1)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))+-1//2*2^(1/2)*pi^(1/2)*cos(1)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))+-1//2*2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1))
@test integrate(x*(1+-1x)^(1/2)*exp(arctanh(x))*sin(x), x) == :((1+x)^(1/2)*cos(x)+-1*(1+x)^3//2*cos(x)+3//2*(1+x)^(1/2)*sin(x)+-3//4*2^(1/2)*pi^(1/2)*cos(1)*fresnels(2^(1/2)*pi^-1//2*(1+x)^(1/2))+-1//2*2^(1/2)*pi^(1/2)*cos(1)*fresnelc(2^(1/2)*pi^-1//2*(1+x)^(1/2))+-1//2*2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*(1+x)^(1/2))*sin(1)+3//4*2^(1/2)*pi^(1/2)*fresnelc(2^(1/2)*pi^-1//2*(1+x)^(1/2))*sin(1))
@test integrate((1+-1x)^(1/2)*exp(arctanh(x))*sin(x), x) == :(-1*(1+x)^(1/2)*cos(x)+(1/2)*2^(1/2)*pi^(1/2)*cos(1)*fresnelc(2^(1/2)*pi^-1//2*(1+x)^(1/2))+(1/2)*2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*(1+x)^(1/2))*sin(1))
@test integrate(x*(1+x)^3//2*exp(arctanh(x))*sin(x), x) == :((1+-1x)^5//2*cos(x)+-5*(1+-1x)^3//2*cos(x)+-15//2*(1+-1x)^(1/2)*sin(x)+5//2*(1+-1x)^3//2*sin(x)+17//4*(1+-1x)^(1/2)*cos(x)+-17//8*2^(1/2)*pi^(1/2)*cos(1)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))+-17//8*2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1)+-1//4*2^(1/2)*pi^(1/2)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1)+1//4*2^(1/2)*pi^(1/2)*cos(1)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2)))
@test integrate((1+x)^3//2*exp(arctanh(x))*sin(x), x) == :(-1*(1+-1x)^3//2*cos(x)+4*(1+-1x)^(1/2)*cos(x)+-3//2*(1+-1x)^(1/2)*sin(x)+-2*2^(1/2)*pi^(1/2)*cos(1)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))+-2*2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1)+-13//4*2^(1/2)*pi^(1/2)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1)+13//4*2^(1/2)*pi^(1/2)*cos(1)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2)))
@test integrate(x*(1+-1x)^3//2*exp(arctanh(x))*sin(x), x) == :((1+x)^5//2*cos(x)+-3*(1+x)^3//2*cos(x)+-7//4*(1+x)^(1/2)*cos(x)+-5//2*(1+x)^3//2*sin(x)+9//2*(1+x)^(1/2)*sin(x)+-9//4*2^(1/2)*pi^(1/2)*cos(1)*fresnels(2^(1/2)*pi^-1//2*(1+x)^(1/2))+7//8*2^(1/2)*pi^(1/2)*cos(1)*fresnelc(2^(1/2)*pi^-1//2*(1+x)^(1/2))+7//8*2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*(1+x)^(1/2))*sin(1)+9//4*2^(1/2)*pi^(1/2)*fresnelc(2^(1/2)*pi^-1//2*(1+x)^(1/2))*sin(1))
@test integrate((1+-1x)^3//2*exp(arctanh(x))*sin(x), x) == :((1+x)^3//2*cos(x)+-2*(1+x)^(1/2)*cos(x)+-3//2*(1+x)^(1/2)*sin(x)+2^(1/2)*pi^(1/2)*cos(1)*fresnelc(2^(1/2)*pi^-1//2*(1+x)^(1/2))+2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*(1+x)^(1/2))*sin(1)+-3//4*2^(1/2)*pi^(1/2)*fresnelc(2^(1/2)*pi^-1//2*(1+x)^(1/2))*sin(1)+3//4*2^(1/2)*pi^(1/2)*cos(1)*fresnels(2^(1/2)*pi^-1//2*(1+x)^(1/2)))
@test integrate(x*(1+x)^-1//2*exp(arctanh(x))*sin(x), x) == :((1+-1x)^(1/2)*cos(x)+2^(1/2)*pi^(1/2)*cos(1)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))+-1*2^(1/2)*pi^(1/2)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1)+-1//2*2^(1/2)*pi^(1/2)*cos(1)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))+-1//2*2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1))
@test integrate((1+x)^-1//2*exp(arctanh(x))*sin(x), x) == :(2^(1/2)*pi^(1/2)*cos(1)*fresnels(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))+-1*2^(1/2)*pi^(1/2)*fresnelc(2^(1/2)*pi^-1//2*(1+-1x)^(1/2))*sin(1))
@test integrate(x^3*exp(arctanh(a+b*x)), x) == :(1//8*b^-4*(3+-12a+-8*a^3+12*a^2)*arcsin(a+b*x)+-1//4*b^-2*x^2*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2)+-1//8*b^-4*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(3+-12a+-8*a^3+12*a^2)+-1//24*b^-4*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2)*(7+-10a+18*a^2+b*x*(2+-12a)))
@test integrate(x^2*exp(arctanh(a+b*x)), x) == :((1/2)*b^-3*(1+-2a+2*a^2)*arcsin(a+b*x)+-1//2*b^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(1+-2a+2*a^2)+-1//3*x*b^-2*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2)+-1//6*b^-3*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2)*(1+-4a))
@test integrate(x*exp(arctanh(a+b*x)), x) == :((1/2)*b^-2*(1+-2a)*arcsin(a+b*x)+-1//2*b^-2*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2)+-1//2*b^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(1+-2a))
@test integrate(exp(arctanh(a+b*x)), x) == :(b^-1*arcsin(a+b*x)+-1*b^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2))
@test integrate(x^-1*exp(arctanh(a+b*x)), x) == :(-1*(1+-1*a^2)^-1//2*(2+2a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+arcsin(a+b*x))
@test integrate(x^-2*exp(arctanh(a+b*x)), x) == :(-1*x^-1*(1+-1a)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)+-2*b*(1+-1a)^-1*(1+-1*a^2)^-1//2*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2))
@test integrate(x^-3*exp(arctanh(a+b*x)), x) == :(-1*x^-2*(2+-2*a^2)^-1*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2)+-1*b^2*(1+a)^-1*(1+-1a)^-2*(1+-1*a^2)^-1//2*(1+2a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+-1//2*b*x^-1*(1+a)^-1*(1+-1a)^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(1+2a))
@test integrate(x^-4*exp(arctanh(a+b*x)), x) == :(-1*x^-3*(3+-3a)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)+-1*b^3*(1+-1a)^-1*(1+-1*a^2)^-5//2*(1+2a+2*a^2)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+-1//6*b*x^-2*(1+a)^-1*(1+-1a)^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(3+2a)+-1//6*b^2*x^-1*(1+a)^-2*(1+-1a)^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(1+2a)*(4+a))
@test integrate(x^4*exp(2*arctanh(a+b*x)), x) == :(-1//5*x^5+-1//2*b^-1*x^4+-1*b^-3*x^2*(1+-1a)^2+-2*x*b^-4*(1+-1a)^3+-2*b^-5*(1+-1a)^4*log(1+-1a+-1*b*x)+-1//3*b^-2*x^3*(2+-2a))
@test integrate(x^3*exp(2*arctanh(a+b*x)), x) == :(-1//4*x^4+-2//3*b^-1*x^3+-1*b^-2*x^2*(1+-1a)+-2*x*b^-3*(1+-1a)^2+-2*b^-4*(1+-1a)^3*log(1+-1a+-1*b*x))
@test integrate(x^2*exp(2*arctanh(a+b*x)), x) == :(-1//3*x^3+-1*b^-1*x^2+-1*x*b^-2*(2+-2a)+-2*b^-3*(1+-1a)^2*log(1+-1a+-1*b*x))
@test integrate(x*exp(2*arctanh(a+b*x)), x) == :(-1//2*x^2+-2*x*b^-1+-1*b^-2*(2+-2a)*log(1+-1a+-1*b*x))
@test integrate(exp(2*arctanh(a+b*x)), x) == :(-1x+-2*b^-1*log(1+-1a+-1*b*x))
@test integrate(x^-1*exp(2*arctanh(a+b*x)), x) == :(-2*(1+-1a)^-1*log(1+-1a+-1*b*x)+(1+-1a)^-1*(1+a)*log(x))
@test integrate(x^-2*exp(2*arctanh(a+b*x)), x) == :(-1*x^-1*(1+-1a)^-1*(1+a)+-2*b*(1+-1a)^-2*log(1+-1a+-1*b*x)+2*b*(1+-1a)^-2*log(x))
@test integrate(x^-3*exp(2*arctanh(a+b*x)), x) == :(-1*x^-2*(2+-2a)^-1*(1+a)+-2*b*x^-1*(1+-1a)^-2+-2*b^2*(1+-1a)^-3*log(1+-1a+-1*b*x)+2*b^2*(1+-1a)^-3*log(x))
@test integrate(x^-4*exp(2*arctanh(a+b*x)), x) == :(-1*b*x^-2*(1+-1a)^-2+-1*x^-3*(3+-3a)^-1*(1+a)+-2*b^2*x^-1*(1+-1a)^-3+-2*b^3*(1+-1a)^-4*log(1+-1a+-1*b*x)+2*b^3*(1+-1a)^-4*log(x))
@test integrate(x^3*exp(3*arctanh(a+b*x)), x) == :(-1//8*b^-4*(51+-132a+-24*a^3+108*a^2)*arcsin(a+b*x)+2*b^-1*x^3*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^-1//2+1//8*b^-4*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(51+-132a+-24*a^3+108*a^2)+1//8*b^-4*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2)*(29+-54a+22*a^2+b*x*(22+-20a))+9//4*b^-2*x^2*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2))
@test integrate(x^2*exp(3*arctanh(a+b*x)), x) == :(-1//2*b^-3*(11+-18a+6*a^2)*arcsin(a+b*x)+1//3*b^-3*(1+a+b*x)^5//2*(1+-1a+-1*b*x)^(1/2)+b^-3*(1+-1a)^2*(1+a+b*x)^5//2*(1+-1a+-1*b*x)^-1//2+(1/2)*b^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(11+-18a+6*a^2)+1//6*b^-3*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2)*(11+-18a+6*a^2))
@test integrate(x*exp(3*arctanh(a+b*x)), x) == :(-1//2*b^-2*(9+-6a)*arcsin(a+b*x)+b^-2*(1+a+b*x)^5//2*(1+-1a+-1*b*x)^-1//2*(1+-1a)+(1/2)*b^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(9+-6a)+(1/2)*b^-2*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^(1/2)*(3+-2a))
@test integrate(exp(3*arctanh(a+b*x)), x) == :(-3*b^-1*arcsin(a+b*x)+2*b^-1*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^-1//2+3*b^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2))
@test integrate(x^-1*exp(3*arctanh(a+b*x)), x) == :(-1*arcsin(a+b*x)+4*(1+-1a)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2+-2*(1+a)^2*(1+-1a)^-1*(1+-1*a^2)^-1//2*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2))
@test integrate(x^-2*exp(3*arctanh(a+b*x)), x) == :(-1*x^-1*(1+-1a)^-1*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^-1//2+6*b*(1+-1a)^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2+-1*b*(1+-1a)^-2*(1+-1*a^2)^-1//2*(6+6a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2))
@test integrate(x^-3*exp(3*arctanh(a+b*x)), x) == :(-1*x^-2*(2+-2*a^2)^-1*(1+a+b*x)^5//2*(1+-1a+-1*b*x)^-1//2+-1*b^2*(1+-1a)^-3*(1+-1*a^2)^-1//2*(9+6a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+b^2*(1+a)^-1*(1+-1a)^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2*(9+6a)+-1//2*b*x^-1*(1+a)^-1*(1+-1a)^-2*(1+a+b*x)^3//2*(1+-1a+-1*b*x)^-1//2*(3+2a))
@test integrate(x^-4*exp(3*arctanh(a+b*x)), x) == :(-1*x^-3*(3+-3a)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2*(1+a)+-7//6*b*x^-2*(1+-1a)^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2+-1*b^3*(1+a)^-1*(1+-1a)^-4*(1+-1*a^2)^-1//2*(11+6*a^2+18a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+1//6*b^3*(1+a)^-1*(1+-1a)^-4*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2*(52+2*a^2+51a)+-1//6*b^2*x^-1*(1+a)^-1*(1+-1a)^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2*(19+16a))
@test integrate(x^3*exp(-1*arctanh(a+b*x)), x) == :(-1//8*b^-4*(3+8*a^3+12a+12*a^2)*arcsin(a+b*x)+-1//4*b^-2*x^2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2+-1//8*b^-4*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(3+8*a^3+12a+12*a^2)+-1//24*b^-4*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2*(7+10a+18*a^2+-1*b*x*(2+12a)))
@test integrate(x^2*exp(-1*arctanh(a+b*x)), x) == :((1/2)*b^-3*(1+2a+2*a^2)*arcsin(a+b*x)+(1/2)*b^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(1+2a+2*a^2)+-1//3*x*b^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2+1//6*b^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2*(1+4a))
@test integrate(x*exp(-1*arctanh(a+b*x)), x) == :(-1//2*b^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2+-1//2*b^-2*(1+2a)*arcsin(a+b*x)+-1//2*b^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(1+2a))
@test integrate(exp(-1*arctanh(a+b*x)), x) == :(b^-1*arcsin(a+b*x)+b^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2))
@test integrate(x^-1*exp(-1*arctanh(a+b*x)), x) == :(-1*arcsin(a+b*x)+-1*(1+-1*a^2)^-1//2*(2+-2a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2))
@test integrate(x^-2*exp(-1*arctanh(a+b*x)), x) == :(-1*x^-1*(1+a)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)+2*b*(1+a)^-1*(1+-1*a^2)^-1//2*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2))
@test integrate(x^-3*exp(-1*arctanh(a+b*x)), x) == :(-1*x^-2*(2+-2*a^2)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2+-1*b^2*(1+a)^-2*(1+-1a)^-1*(1+-1*a^2)^-1//2*(1+-2a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+b*x^-1*(1+a)^-2*(2+-2a)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(1+-2a))
@test integrate(x^-4*exp(-1*arctanh(a+b*x)), x) == :(-1*x^-3*(3+3a)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)+b^3*(1+a)^-1*(1+-1*a^2)^-5//2*(1+-2a+2*a^2)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+b*x^-2*(1+a)^-2*(6+-6a)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(3+-2a)+-1//6*b^2*x^-1*(1+a)^-3*(1+-1a)^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(1+-2a)*(4+-1a))
@test integrate(x^4*exp(-2*arctanh(a+b*x)), x) == :(-1//5*x^5+(1/2)*b^-1*x^4+b^-3*x^2*(1+a)^2+-2*x*b^-4*(1+a)^3+2*b^-5*(1+a)^4*log(1+a+b*x)+-1//3*b^-2*x^3*(2+2a))
@test integrate(x^3*exp(-2*arctanh(a+b*x)), x) == :(-1//4*x^4+2//3*b^-1*x^3+-1*b^-2*x^2*(1+a)+-2*b^-4*(1+a)^3*log(1+a+b*x)+2*x*b^-3*(1+a)^2)
@test integrate(x^2*exp(-2*arctanh(a+b*x)), x) == :(-1//3*x^3+b^-1*x^2+-1*x*b^-2*(2+2a)+2*b^-3*(1+a)^2*log(1+a+b*x))
@test integrate(x*exp(-2*arctanh(a+b*x)), x) == :(-1//2*x^2+2*x*b^-1+-1*b^-2*(2+2a)*log(1+a+b*x))
@test integrate(exp(-2*arctanh(a+b*x)), x) == :(-1x+2*b^-1*log(1+a+b*x))
@test integrate(x^-1*exp(-2*arctanh(a+b*x)), x) == :(-2*(1+a)^-1*log(1+a+b*x)+(1+a)^-1*(1+-1a)*log(x))
@test integrate(x^-2*exp(-2*arctanh(a+b*x)), x) == :(-1*x^-1*(1+a)^-1*(1+-1a)+-2*b*(1+a)^-2*log(x)+2*b*(1+a)^-2*log(1+a+b*x))
@test integrate(x^-3*exp(-2*arctanh(a+b*x)), x) == :(-1*x^-2*(2+2a)^-1*(1+-1a)+-2*b^2*(1+a)^-3*log(1+a+b*x)+2*b*x^-1*(1+a)^-2+2*b^2*(1+a)^-3*log(x))
@test integrate(x^-4*exp(-2*arctanh(a+b*x)), x) == :(b*x^-2*(1+a)^-2+-1*x^-3*(3+3a)^-1*(1+-1a)+-2*b^2*x^-1*(1+a)^-3+-2*b^3*(1+a)^-4*log(x)+2*b^3*(1+a)^-4*log(1+a+b*x))
@test integrate(x^3*exp(-3*arctanh(a+b*x)), x) == :(1//8*b^-4*(51+24*a^3+108*a^2+132a)*arcsin(a+b*x)+-2*b^-1*x^3*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^3//2+1//8*b^-4*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(51+24*a^3+108*a^2+132a)+1//8*b^-4*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2*(29+22*a^2+54a+-1*b*x*(22+20a))+9//4*b^-2*x^2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2)
@test integrate(x^2*exp(-3*arctanh(a+b*x)), x) == :(-1//2*b^-3*(11+6*a^2+18a)*arcsin(a+b*x)+-1//3*b^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^5//2+-1*b^-3*(1+a)^2*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^5//2+-1//2*b^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(11+6*a^2+18a)+-1//6*b^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2*(11+6*a^2+18a))
@test integrate(x*exp(-3*arctanh(a+b*x)), x) == :((1/2)*b^-2*(9+6a)*arcsin(a+b*x)+b^-2*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^5//2*(1+a)+(1/2)*b^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*(9+6a)+(1/2)*b^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^3//2*(3+2a))
@test integrate(exp(-3*arctanh(a+b*x)), x) == :(-3*b^-1*arcsin(a+b*x)+-3*b^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)+-2*b^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^3//2)
@test integrate(x^-1*exp(-3*arctanh(a+b*x)), x) == :(4*(1+a)^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^(1/2)+-2*(1+a)^-1*(1+-1a)^2*(1+-1*a^2)^-1//2*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+arcsin(a+b*x))
@test integrate(x^-2*exp(-3*arctanh(a+b*x)), x) == :(-1*x^-1*(1+a)^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^3//2+-6*b*(1+a)^-2*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^(1/2)+b*(1+a)^-2*(1+-1*a^2)^-1//2*(6+-6a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2))
@test integrate(x^-3*exp(-3*arctanh(a+b*x)), x) == :(-1*x^-2*(2+-2*a^2)^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^5//2+-1*b^2*(1+a)^-3*(1+-1*a^2)^-1//2*(9+-6a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+b^2*(1+a)^-3*(1+-1a)^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^(1/2)*(9+-6a)+b*x^-1*(1+a)^-2*(2+-2a)^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^3//2*(3+-2a))
@test integrate(x^-4*exp(-3*arctanh(a+b*x)), x) == :(-1*x^-3*(3+3a)^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^(1/2)*(1+-1a)+7//6*b*x^-2*(1+a)^-2*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^(1/2)+b^3*(1+a)^-4*(1+-1a)^-1*(1+-1*a^2)^-1//2*(11+-18a+6*a^2)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)+-1*b^3*(1+a)^-4*(6+-6a)^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^(1/2)*(52+-51a+2*a^2)+-1*b^2*x^-1*(1+a)^-3*(6+-6a)^-1*(1+a+b*x)^-1//2*(1+-1a+-1*b*x)^(1/2)*(19+-16a))
@test integrate((2+b*x)^-1*exp(arctanh(1+b*x)), x) == :(b^-1*arcsin(1+b*x))
@test integrate(x^3*(1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1*exp(arctanh(a+b*x)), x) == :(-1//2*b^-4*(3+-6a+6*a^2)*arcsin(a+b*x)+(1/2)*b^-4*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)*((1+-2a)*(4+-1a)+b*x*(3+-2a))+b^-2*x^2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2*(1+-1a))
@test integrate(x^2*(1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1*exp(arctanh(a+b*x)), x) == :(b^-3*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^(1/2)+-1*b^-3*(1+-2a)*arcsin(a+b*x)+b^-3*(1+-1a)^2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)
@test integrate(x*(1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1*exp(arctanh(a+b*x)), x) == :(-1*b^-2*arcsin(a+b*x)+b^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2*(1+-1a))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1*exp(arctanh(a+b*x)), x) == :(b^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2)
@test integrate(x^-1*(1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1*exp(arctanh(a+b*x)), x) == :((1+-1a)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2+-2*(1+-1a)^-1*(1+-1*a^2)^-1//2*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2))
@test integrate(x^-2*(1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1*exp(arctanh(a+b*x)), x) == :(-1*x^-1*(1+-1*a^2)^-1*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2+b*(1+a)^-1*(1+-1a)^-2*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2*(2+a)+-1*b*(1+a)^-1*(1+-1a)^-2*(1+-1*a^2)^-1//2*(2+4a)*arctanh((1+a)^-1//2*(1+-1a)^(1/2)*(1+a+b*x)^(1/2)*(1+-1a+-1*b*x)^-1//2))
@test integrate((c+-1*c*a^2*x^2)^4*exp(arctanh(a*x)), x) == :(-1//9*a^-1*c^4*(1+-1*a^2*x^2)^9//2+1//8*x*c^4*(1+-1*a^2*x^2)^7//2+7//48*x*c^4*(1+-1*a^2*x^2)^5//2+35//128*x*c^4*(1+-1*a^2*x^2)^(1/2)+35//128*a^-1*c^4*arcsin(a*x)+35//192*x*c^4*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^3*exp(arctanh(a*x)), x) == :(-1//7*a^-1*c^3*(1+-1*a^2*x^2)^7//2+1//6*x*c^3*(1+-1*a^2*x^2)^5//2+5//16*x*c^3*(1+-1*a^2*x^2)^(1/2)+5//16*a^-1*c^3*arcsin(a*x)+5//24*x*c^3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^2*exp(arctanh(a*x)), x) == :(-1//5*a^-1*c^2*(1+-1*a^2*x^2)^5//2+1//4*x*c^2*(1+-1*a^2*x^2)^3//2+3//8*x*c^2*(1+-1*a^2*x^2)^(1/2)+3//8*a^-1*c^2*arcsin(a*x))
@test integrate((c+-1*c*a^2*x^2)*exp(arctanh(a*x)), x) == :((1/2)*c*x*(1+-1*a^2*x^2)^(1/2)+(1/2)*c*a^-1*arcsin(a*x)+-1//3*c*a^-1*(1+-1*a^2*x^2)^3//2)
@test integrate(x^4*(c+-1*c*a^2*x^2)^-1*exp(arctanh(a*x)), x) == :(-3//2*a^-5*c^-1*arcsin(a*x)+1//6*a^-5*c^-1*(1+-1*a^2*x^2)^(1/2)*(16+9*a*x)+4//3*a^-3*c^-1*x^2*(1+-1*a^2*x^2)^(1/2)+a^-2*c^-1*x^3*(1+-1*a^2*x^2)^-1//2*(1+a*x))
@test integrate(x^3*(c+-1*c*a^2*x^2)^-1*exp(arctanh(a*x)), x) == :(-3//2*a^-4*c^-1*arcsin(a*x)+(1/2)*a^-4*c^-1*(1+-1*a^2*x^2)^(1/2)*(4+3*a*x)+a^-2*c^-1*x^2*(1+-1*a^2*x^2)^-1//2*(1+a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-1*exp(arctanh(a*x)), x) == :(a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)+-1*a^-3*c^-1*arcsin(a*x)+a^-3*c^-1*(1+-1*a^2*x^2)^-1//2*(1+a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-1*exp(arctanh(a*x)), x) == :(-1*a^-2*c^-1*arcsin(a*x)+a^-2*c^-1*(1+-1*a^2*x^2)^-1//2*(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^-1*exp(arctanh(a*x)), x) == :(a^-1*c^-1*exp(arctanh(a*x)))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-1*exp(arctanh(a*x)), x) == :(-1*c^-1*arctanh((1+-1*a^2*x^2)^(1/2))+c^-1*(1+-1*a^2*x^2)^-1//2*(1+a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-1*exp(arctanh(a*x)), x) == :(-1*a*c^-1*arctanh((1+-1*a^2*x^2)^(1/2))+-2*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2)+c^-1*x^-1*(1+-1*a^2*x^2)^-1//2*(1+a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-1*exp(arctanh(a*x)), x) == :(-3//2*a^2*c^-1*arctanh((1+-1*a^2*x^2)^(1/2))+-3//2*c^-1*x^-2*(1+-1*a^2*x^2)^(1/2)+c^-1*x^-2*(1+-1*a^2*x^2)^-1//2*(1+a*x)+-2*a*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^-1*exp(arctanh(a*x)), x) == :(-4//3*c^-1*x^-3*(1+-1*a^2*x^2)^(1/2)+-3//2*a^3*c^-1*arctanh((1+-1*a^2*x^2)^(1/2))+c^-1*x^-3*(1+-1*a^2*x^2)^-1//2*(1+a*x)+-8//3*a^2*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2)+-3//2*a*c^-1*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^6*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(5//2*a^-7*c^-2*arcsin(a*x)+-8//3*a^-5*c^-2*x^2*(1+-1*a^2*x^2)^(1/2)+-1//6*a^-7*c^-2*(1+-1*a^2*x^2)^(1/2)*(32+15*a*x)+-1//3*a^-4*c^-2*x^3*(1+-1*a^2*x^2)^-1//2*(5+6*a*x)+1//3*a^-2*c^-2*x^5*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate(x^5*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(5//2*a^-6*c^-2*arcsin(a*x)+-1//6*a^-6*c^-2*(1+-1*a^2*x^2)^(1/2)*(16+15*a*x)+-1//3*a^-4*c^-2*x^2*(1+-1*a^2*x^2)^-1//2*(4+5*a*x)+1//3*a^-2*c^-2*x^4*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate(x^4*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(a^-5*c^-2*arcsin(a*x)+-8//3*a^-5*c^-2*(1+-1*a^2*x^2)^(1/2)+-1//3*x*a^-4*c^-2*(1+-1*a^2*x^2)^-1//2*(3+4*a*x)+1//3*a^-2*c^-2*x^3*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate(x^3*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(a^-4*c^-2*arcsin(a*x)+-1//3*a^-4*c^-2*(1+-1*a^2*x^2)^-1//2*(2+3*a*x)+1//3*a^-2*c^-2*x^2*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(-2//3*a^-3*c^-2*(1+-1*a^2*x^2)^-1//2+1//3*a^-1*c^-2*x^2*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(-1//3*x*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2+1//3*a^-2*c^-2*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(2//3*x*c^-2*(1+-1*a^2*x^2)^-1//2+1//3*a^-1*c^-2*(1+-1*a^2*x^2)^-3//2*(1+a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(-1*c^-2*arctanh((1+-1*a^2*x^2)^(1/2))+1//3*c^-2*(1+-1*a^2*x^2)^-3//2*(1+a*x)+1//3*c^-2*(1+-1*a^2*x^2)^-1//2*(3+2*a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(-1*a*c^-2*arctanh((1+-1*a^2*x^2)^(1/2))+-8//3*c^-2*x^-1*(1+-1*a^2*x^2)^(1/2)+1//3*c^-2*x^-1*(1+-1*a^2*x^2)^-3//2*(1+a*x)+1//3*c^-2*x^-1*(1+-1*a^2*x^2)^-1//2*(4+3*a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(-5//2*a^2*c^-2*arctanh((1+-1*a^2*x^2)^(1/2))+-5//2*c^-2*x^-2*(1+-1*a^2*x^2)^(1/2)+-8//3*a*c^-2*x^-1*(1+-1*a^2*x^2)^(1/2)+1//3*c^-2*x^-2*(1+-1*a^2*x^2)^-3//2*(1+a*x)+1//3*c^-2*x^-2*(1+-1*a^2*x^2)^-1//2*(5+4*a*x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^-2*exp(arctanh(a*x)), x) == :(-8//3*c^-2*x^-3*(1+-1*a^2*x^2)^(1/2)+-5//2*a^3*c^-2*arctanh((1+-1*a^2*x^2)^(1/2))+-16//3*a^2*c^-2*x^-1*(1+-1*a^2*x^2)^(1/2)+-5//2*a*c^-2*x^-2*(1+-1*a^2*x^2)^(1/2)+1//3*c^-2*x^-3*(1+-1*a^2*x^2)^-3//2*(1+a*x)+1//3*c^-2*x^-3*(1+-1*a^2*x^2)^-1//2*(6+5*a*x))
@test integrate(x^7*(c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(-7//2*a^-8*c^-3*arcsin(a*x)+1//10*a^-8*c^-3*(1+-1*a^2*x^2)^(1/2)*(32+35*a*x)+-1//15*a^-4*c^-3*x^4*(1+-1*a^2*x^2)^-3//2*(6+7*a*x)+1//5*a^-2*c^-3*x^6*(1+-1*a^2*x^2)^-5//2*(1+a*x)+1//15*a^-6*c^-3*x^2*(1+-1*a^2*x^2)^-1//2*(24+35*a*x))
@test integrate(x^6*(c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(-1*a^-7*c^-3*arcsin(a*x)+16//5*a^-7*c^-3*(1+-1*a^2*x^2)^(1/2)+-1//15*a^-4*c^-3*x^3*(1+-1*a^2*x^2)^-3//2*(5+6*a*x)+1//5*x*a^-6*c^-3*(1+-1*a^2*x^2)^-1//2*(5+8*a*x)+1//5*a^-2*c^-3*x^5*(1+-1*a^2*x^2)^-5//2*(1+a*x))
@test integrate(x^5*(c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(-1*a^-6*c^-3*arcsin(a*x)+1//15*a^-6*c^-3*(1+-1*a^2*x^2)^-1//2*(8+15*a*x)+-1//15*a^-4*c^-3*x^2*(1+-1*a^2*x^2)^-3//2*(4+5*a*x)+1//5*a^-2*c^-3*x^4*(1+-1*a^2*x^2)^-5//2*(1+a*x))
@test integrate(x^4*(c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(-4//15*a^-5*c^-3*(1+-1*a^2*x^2)^-3//2+4//5*a^-5*c^-3*(1+-1*a^2*x^2)^-1//2+1//5*a^-1*c^-3*x^4*(1+-1*a^2*x^2)^-5//2*(1+a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(-2//15*x*a^-2*c^-3*(1+-1*a^2*x^2)^-1//2+-1//15*a^-3*c^-3*(1+-1*a^2*x^2)^-3//2*(2+-2*a*x)+1//5*a^-1*c^-3*x^2*(1+-1*a^2*x^2)^-5//2*(1+a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(-2//15*x*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2+-1//15*x*a^-1*c^-3*(1+-1*a^2*x^2)^-3//2+1//5*a^-2*c^-3*(1+-1*a^2*x^2)^-5//2*(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(4//15*x*c^-3*(1+-1*a^2*x^2)^-3//2+8//15*x*c^-3*(1+-1*a^2*x^2)^-1//2+1//5*a^-1*c^-3*(1+-1*a^2*x^2)^-5//2*(1+a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(-1*c^-3*arctanh((1+-1*a^2*x^2)^(1/2))+1//5*c^-3*(1+-1*a^2*x^2)^-5//2*(1+a*x)+1//15*c^-3*(1+-1*a^2*x^2)^-3//2*(5+4*a*x)+1//15*c^-3*(1+-1*a^2*x^2)^-1//2*(15+8*a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(-1*a*c^-3*arctanh((1+-1*a^2*x^2)^(1/2))+-16//5*c^-3*x^-1*(1+-1*a^2*x^2)^(1/2)+1//5*c^-3*x^-1*(1+-1*a^2*x^2)^-5//2*(1+a*x)+1//5*c^-3*x^-1*(1+-1*a^2*x^2)^-1//2*(8+5*a*x)+1//15*c^-3*x^-1*(1+-1*a^2*x^2)^-3//2*(6+5*a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-3*exp(arctanh(a*x)), x) == :(-7//2*a^2*c^-3*arctanh((1+-1*a^2*x^2)^(1/2))+-7//2*c^-3*x^-2*(1+-1*a^2*x^2)^(1/2)+-16//5*a*c^-3*x^-1*(1+-1*a^2*x^2)^(1/2)+1//5*c^-3*x^-2*(1+-1*a^2*x^2)^-5//2*(1+a*x)+1//15*c^-3*x^-2*(1+-1*a^2*x^2)^-3//2*(7+6*a*x)+1//15*c^-3*x^-2*(1+-1*a^2*x^2)^-1//2*(35+24*a*x))
@test integrate((c+-1*c*a^2*x^2)^-4*exp(arctanh(a*x)), x) == :(6//35*x*c^-4*(1+-1*a^2*x^2)^-5//2+8//35*x*c^-4*(1+-1*a^2*x^2)^-3//2+16//35*x*c^-4*(1+-1*a^2*x^2)^-1//2+1//7*a^-1*c^-4*(1+-1*a^2*x^2)^-7//2*(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^-5*exp(arctanh(a*x)), x) == :(8//63*x*c^-5*(1+-1*a^2*x^2)^-7//2+16//105*x*c^-5*(1+-1*a^2*x^2)^-5//2+64//315*x*c^-5*(1+-1*a^2*x^2)^-3//2+128//315*x*c^-5*(1+-1*a^2*x^2)^-1//2+1//9*a^-1*c^-5*(1+-1*a^2*x^2)^-9//2*(1+a*x))
@test integrate(x^4*(1+-1*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x*a^-4+-1*a^-5*log(1+-1*a*x)+-1//2*a^-3*x^2+-1//3*a^-2*x^3+-1//4*a^-1*x^4)
@test integrate(x^3*(1+-1*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x*a^-3+-1*a^-4*log(1+-1*a*x)+-1//2*a^-2*x^2+-1//3*a^-1*x^3)
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x*a^-2+-1*a^-3*log(1+-1*a*x)+-1//2*a^-1*x^2)
@test integrate(x*(1+-1*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x*a^-1+-1*a^-2*log(1+-1*a*x))
@test integrate((1+-1*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*a^-1*log(1+-1*a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*log(1+-1*a*x)+log(x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x^-1+a*log(x)+-1*a*log(1+-1*a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1//2*x^-2+a^2*log(x)+-1*a*x^-1+-1*a^2*log(1+-1*a*x))
@test integrate(x^-4*(1+-1*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1//3*x^-3+a^3*log(x)+-1*a^2*x^-1+-1*a^3*log(1+-1*a*x)+-1//2*a*x^-2)
@test integrate(x^4*(1+-1*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(x*a^-4+(1/2)*a^-5*(1+-1*a*x)^-1+(1/2)*a^-3*x^2+1//4*a^-5*log(1+a*x)+7//4*a^-5*log(1+-1*a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(x*a^-3+(1/2)*a^-4*(1+-1*a*x)^-1+-1//4*a^-4*log(1+a*x)+5//4*a^-4*log(1+-1*a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :((1/2)*a^-3*(1+-1*a*x)^-1+1//4*a^-3*log(1+a*x)+3//4*a^-3*log(1+-1*a*x))
@test integrate(x*(1+-1*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :((1/2)*a^-2*(1+-1*a*x)^-1+-1//2*a^-2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :((1/2)*a^-1*(1+-1*a*x)^-1+(1/2)*a^-1*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :((2+-2*a*x)^-1+-3//4*log(1+-1*a*x)+-1//4*log(1+a*x)+log(x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(-1*x^-1+a*(2+-2*a*x)^-1+a*log(x)+-5//4*a*log(1+-1*a*x)+1//4*a*log(1+a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(-1//2*x^-2+a^2*(2+-2*a*x)^-1+-1*a*x^-1+2*a^2*log(x)+-7//4*a^2*log(1+-1*a*x)+-1//4*a^2*log(1+a*x))
@test integrate(x^-4*(1+-1*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(-1//3*x^-3+a^3*(2+-2*a*x)^-1+-2*a^2*x^-1+2*a^3*log(x)+-9//4*a^3*log(1+-1*a*x)+-1//2*a*x^-2+1//4*a^3*log(1+a*x))
@test integrate(x^6*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1*x*a^-6+-39//16*a^-7*log(1+-1*a*x)+-9//16*a^-7*log(1+a*x)+-5//4*a^-7*(1+-1*a*x)^-1+-1//2*a^-5*x^2+-1//8*a^-7*(1+a*x)^-1+1//8*a^-7*(1+-1*a*x)^-2)
@test integrate(x^5*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1*x*a^-5+-1*a^-6*(1+-1*a*x)^-1+-23//16*a^-6*log(1+-1*a*x)+1//8*a^-6*(1+a*x)^-1+1//8*a^-6*(1+-1*a*x)^-2+7//16*a^-6*log(1+a*x))
@test integrate(x^4*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-11//16*a^-5*log(1+-1*a*x)+-5//16*a^-5*log(1+a*x)+-3//4*a^-5*(1+-1*a*x)^-1+-1//8*a^-5*(1+a*x)^-1+1//8*a^-5*(1+-1*a*x)^-2)
@test integrate(x^3*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//2*a^-4*(1+-1*a*x)^-1+1//8*a^-4*(1+a*x)^-1+1//8*a^-4*(1+-1*a*x)^-2+3//8*a^-4*arctanh(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//4*a^-3*(1+-1*a*x)^-1+-1//8*a^-3*(1+a*x)^-1+-1//8*a^-3*arctanh(a*x)+1//8*a^-3*(1+-1*a*x)^-2)
@test integrate(x*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//8*a^-2*arctanh(a*x)+1//8*a^-2*(1+a*x)^-1+1//8*a^-2*(1+-1*a*x)^-2)
@test integrate((1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//8*a^-1*(1+a*x)^-1+1//4*a^-1*(1+-1*a*x)^-1+1//8*a^-1*(1+-1*a*x)^-2+3//8*a^-1*arctanh(a*x))
@test integrate(x^-1*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :((2+-2*a*x)^-1+(8+8*a*x)^-1+-11//16*log(1+-1*a*x)+-5//16*log(1+a*x)+1//8*(1+-1*a*x)^-2+log(x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1*x^-1+a*log(x)+-1*a*(8+8*a*x)^-1+3*a*(4+-4*a*x)^-1+-23//16*a*log(1+-1*a*x)+1//8*a*(1+-1*a*x)^-2+7//16*a*log(1+a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//2*x^-2+a^2*(1+-1*a*x)^-1+a^2*(8+8*a*x)^-1+-1*a*x^-1+3*a^2*log(x)+-39//16*a^2*log(1+-1*a*x)+-9//16*a^2*log(1+a*x)+1//8*a^2*(1+-1*a*x)^-2)
@test integrate(x^-4*(1+-1*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//3*x^-3+-1*a^3*(8+8*a*x)^-1+-3*a^2*x^-1+3*a^3*log(x)+5*a^3*(4+-4*a*x)^-1+-59//16*a^3*log(1+-1*a*x)+-1//2*a*x^-2+1//8*a^3*(1+-1*a*x)^-2+11//16*a^3*log(1+a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(arctanh(a*x)), x) == :(1//3*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//4*a*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(arctanh(a*x)), x) == :((1/2)*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//3*a*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(arctanh(a*x)), x) == :(x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(arctanh(a*x)), x) == :((1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(arctanh(a*x)), x) == :(-1*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+a*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(arctanh(a*x)), x) == :(-1//4*c*a^-1*(1+a*x)^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+2//3*c*a^-1*(1+a*x)^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(arctanh(a*x)), x) == :(a^-1*c^2*(1+a*x)^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4//5*a^-1*c^2*(1+a*x)^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//6*a^-1*c^2*(1+a*x)^6*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(arctanh(a*x)), x) == :(-2*a^-1*c^3*(1+a*x)^6*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//8*a^-1*c^3*(1+a*x)^8*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+6//7*a^-1*c^3*(1+a*x)^7*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+8//5*a^-1*c^3*(1+a*x)^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^4*(c+-1*c*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x*a^-4*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1*a^-5*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-1//2*a^-3*x^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//3*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//4*a^-1*x^4*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate(x^3*(c+-1*c*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x*a^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1*a^-4*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-1//2*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//3*a^-1*x^3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate(x^2*(c+-1*c*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x*a^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1*a^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-1//2*a^-1*x^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate(x*(c+-1*c*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1*a^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :((1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+a*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+-1*a*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+a^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+-1*a*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1*a^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^-1//2*exp(arctanh(a*x)), x) == :(-1//3*x^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+a^3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+-1*a^2*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1*a^3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-1//2*a*x^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate(x^5*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :((1/2)*a^-6*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+(1/2)*a^-4*c^-1*x^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+2*x*a^-5*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//4*a^-6*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+1//3*a^-3*c^-1*x^3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+9//4*a^-6*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x^4*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(x*a^-4*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+(1/2)*a^-5*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+(1/2)*a^-3*c^-1*x^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//4*a^-5*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+7//4*a^-5*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x^3*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(x*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+(1/2)*a^-4*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//4*a^-4*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+5//4*a^-4*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :((1/2)*a^-3*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//4*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+3//4*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :((1/2)*a^-2*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//2*a^-2*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :((1/2)*a^-1*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+(1/2)*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+(1/2)*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-3//4*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-1//4*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(-1*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+a*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+(1/2)*a*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-5//4*a*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+1//4*a*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(-1//2*c^-1*x^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+(1/2)*a^2*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1*a*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+2*a^2*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+-7//4*a^2*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-1//4*a^2*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :(-1//3*c^-1*x^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+(1/2)*a^3*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-2*a^2*c^-1*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+2*a^3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+-9//4*a^3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-1//2*a*c^-1*x^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//4*a^3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x))
@test integrate(x^6*(c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1*x*a^-6*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-39//16*a^-7*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-9//16*a^-7*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+-5//4*a^-7*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//2*a^-5*c^-2*x^2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//8*a^-7*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-7*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate(x^5*(c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1*x*a^-5*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1*a^-6*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-23//16*a^-6*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+1//8*a^-6*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-6*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+7//16*a^-6*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x))
@test integrate(x^4*(c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-11//16*a^-5*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-5//16*a^-5*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+-3//4*a^-5*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//8*a^-5*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-5*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate(x^3*(c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//2*a^-4*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-4*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-4*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+3//8*a^-4*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//4*a^-3*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//8*a^-3*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//8*a^-3*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x)+1//8*a^-3*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate(x*(c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//8*a^-2*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x)+1//8*a^-2*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-2*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//8*a^-1*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//4*a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-1*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+3//8*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+(1/2)*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-11//16*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-5//16*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+1//8*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1*c^-2*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+a*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+-23//16*a*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-1//8*a*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+3//4*a*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+7//16*a*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-5//2*exp(arctanh(a*x)), x) == :(-1//2*c^-2*x^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+a^2*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1*a*c^-2*x^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+3*a^2*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(x)+-39//16*a^2*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+-9//16*a^2*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+1//8*a^2*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^2*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(arctanh(a*x)), x) == :(-1//8*a^-1*c^-3*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//32*a^-1*c^-3*(1+a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//24*a^-1*c^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+3//16*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+3//32*a^-1*c^-3*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+5//16*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate(x^m*(1+-1*a^2*x^2)^5//2*exp(arctanh(a*x)), x) == :(x^(1+m)*(1+m)^-1+a*x^(2+m)*(2+m)^-1+a^4*x^(5+m)*(5+m)^-1+a^5*x^(6+m)*(6+m)^-1+-2*a^2*x^(3+m)*(3+m)^-1+-2*a^3*x^(4+m)*(4+m)^-1)
@test integrate(x^m*(1+-1*a^2*x^2)^3//2*exp(arctanh(a*x)), x) == :(x^(1+m)*(1+m)^-1+a*x^(2+m)*(2+m)^-1+-1*a^2*x^(3+m)*(3+m)^-1+-1*a^3*x^(4+m)*(4+m)^-1)
@test integrate(x^m*(1+-1*a^2*x^2)^(1/2)*exp(arctanh(a*x)), x) == :(x^(1+m)*(1+m)^-1+a*x^(2+m)*(2+m)^-1)
@test integrate(x^m*(c+-1*c*a^2*x^2)^5//2*exp(arctanh(a*x)), x) == :(c^2*x^(1+m)*(1+m)^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+a*c^2*x^(2+m)*(1+-1*a^2*x^2)^-1//2*(2+m)^-1*(c+-1*c*a^2*x^2)^(1/2)+a^4*c^2*x^(5+m)*(1+-1*a^2*x^2)^-1//2*(5+m)^-1*(c+-1*c*a^2*x^2)^(1/2)+a^5*c^2*x^(6+m)*(1+-1*a^2*x^2)^-1//2*(6+m)^-1*(c+-1*c*a^2*x^2)^(1/2)+-2*a^2*c^2*x^(3+m)*(1+-1*a^2*x^2)^-1//2*(3+m)^-1*(c+-1*c*a^2*x^2)^(1/2)+-2*a^3*c^2*x^(4+m)*(1+-1*a^2*x^2)^-1//2*(4+m)^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^m*(c+-1*c*a^2*x^2)^3//2*exp(arctanh(a*x)), x) == :(c*x^(1+m)*(1+m)^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+a*c*x^(2+m)*(1+-1*a^2*x^2)^-1//2*(2+m)^-1*(c+-1*c*a^2*x^2)^(1/2)+-1*c*a^2*x^(3+m)*(1+-1*a^2*x^2)^-1//2*(3+m)^-1*(c+-1*c*a^2*x^2)^(1/2)+-1*c*a^3*x^(4+m)*(1+-1*a^2*x^2)^-1//2*(4+m)^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^m*(c+-1*c*a^2*x^2)^(1/2)*exp(arctanh(a*x)), x) == :(x^(1+m)*(1+m)^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+a*x^(2+m)*(1+-1*a^2*x^2)^-1//2*(2+m)^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^4*(c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :(1//5*c*x^5+1//3*a*c*x^6+1//7*c*a^2*x^7)
@test integrate(x^3*(c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :(1//4*c*x^4+1//6*c*a^2*x^6+2//5*a*c*x^5)
@test integrate(x^2*(c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :(1//3*c*x^3+(1/2)*a*c*x^4+1//5*c*a^2*x^5)
@test integrate(x*(c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :((1/2)*c*x^2+1//4*c*a^2*x^4+2//3*a*c*x^3)
@test integrate((c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :(1//3*c*a^-1*(1+a*x)^3)
@test integrate(x^-1*(c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :(c*log(x)+(1/2)*c*a^2*x^2+2*a*c*x)
@test integrate(x^-2*(c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :(-1*c*x^-1+c*x*a^2+2*a*c*log(x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :(-1//2*c*x^-2+c*a^2*log(x)+-2*a*c*x^-1)
@test integrate(x^-4*(c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :(-1//3*c*x^-3*(1+a*x)^3)
@test integrate(x^4*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(1//5*c^2*x^5+-1//4*a^3*c^2*x^8+-1//9*a^4*c^2*x^9+1//3*a*c^2*x^6)
@test integrate(x^3*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(1//4*c^2*x^4+-2//7*a^3*c^2*x^7+-1//8*a^4*c^2*x^8+2//5*a*c^2*x^5)
@test integrate(x^2*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(1//3*c^2*x^3+(1/2)*a*c^2*x^4+-1//3*a^3*c^2*x^6+-1//7*a^4*c^2*x^7)
@test integrate(x*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :((1/2)*c^2*x^2+-2//5*a^3*c^2*x^5+-1//6*a^4*c^2*x^6+2//3*a*c^2*x^3)
@test integrate((c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :((1/2)*a^-1*c^2*(1+a*x)^4+-1//5*a^-1*c^2*(1+a*x)^5)
@test integrate(x^-1*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(c^2*log(x)+2*a*x*c^2+-2//3*a^3*c^2*x^3+-1//4*a^4*c^2*x^4)
@test integrate(x^-2*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(-1*c^2*x^-1+-1*a^3*c^2*x^2+2*a*c^2*log(x)+-1//3*a^4*c^2*x^3)
@test integrate(x^-3*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(-1//2*c^2*x^-2*(1+a*x)^4)
@test integrate(x^-4*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(-1//3*c^2*x^-3+-1*a*c^2*x^-2+-1*x*a^4*c^2+-2*a^3*c^2*log(x))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(-1//4*c^2*x^-4+-1*a^4*c^2*log(x)+2*a^3*c^2*x^-1+-2//3*a*c^2*x^-3)
@test integrate(x^-6*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(-1//5*c^2*x^-5+a^3*c^2*x^-2+a^4*c^2*x^-1+-1//2*a*c^2*x^-4)
@test integrate(x^4*(c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(1//5*c^3*x^5+-1//2*a^3*c^3*x^8+-1//7*a^2*c^3*x^7+-1//9*a^4*c^3*x^9+1//3*a*c^3*x^6+1//5*a^5*c^3*x^10+1//11*a^6*c^3*x^11)
@test integrate(x^3*(c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(1//4*c^3*x^4+-4//7*a^3*c^3*x^7+-1//6*a^2*c^3*x^6+-1//8*a^4*c^3*x^8+1//10*a^6*c^3*x^10+2//5*a*c^3*x^5+2//9*a^5*c^3*x^9)
@test integrate(x^2*(c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(-2*a^-3*c^3*(1+a*x)^6+-3//4*a^-3*c^3*(1+a*x)^8+1//9*a^-3*c^3*(1+a*x)^9+4//5*a^-3*c^3*(1+a*x)^5+13//7*a^-3*c^3*(1+a*x)^7)
@test integrate(x*(c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(-5//7*a^-2*c^3*(1+a*x)^7+-4//5*a^-2*c^3*(1+a*x)^5+1//8*a^-2*c^3*(1+a*x)^8+4//3*a^-2*c^3*(1+a*x)^6)
@test integrate((c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(-2//3*a^-1*c^3*(1+a*x)^6+1//7*a^-1*c^3*(1+a*x)^7+4//5*a^-1*c^3*(1+a*x)^5)
@test integrate(x^-1*(c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(c^3*log(x)+2*a*x*c^3+-4//3*a^3*c^3*x^3+-1//2*a^2*c^3*x^2+-1//4*a^4*c^3*x^4+1//6*a^6*c^3*x^6+2//5*a^5*c^3*x^5)
@test integrate(x^-2*(c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(-1*c^3*x^-1+(1/2)*a^5*c^3*x^4+-1*x*a^2*c^3+-2*a^3*c^3*x^2+2*a*c^3*log(x)+-1//3*a^4*c^3*x^3+1//5*a^6*c^3*x^5)
@test integrate(x^-3*(c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(-1//2*c^3*x^-2+-1*a^2*c^3*log(x)+-4*x*a^3*c^3+-2*a*c^3*x^-1+-1//2*a^4*c^3*x^2+1//4*a^6*c^3*x^4+2//3*a^5*c^3*x^3)
@test integrate(x^-4*(c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(-1//3*c^3*x^-3+a^2*c^3*x^-1+a^5*c^3*x^2+-1*a*c^3*x^-2+-1*x*a^4*c^3+-4*a^3*c^3*log(x)+1//3*a^6*c^3*x^3)
@test integrate((c+-1*c*a^2*x^2)^4*exp(2*arctanh(a*x)), x) == :(-12//7*a^-1*c^4*(1+a*x)^7+-1//9*a^-1*c^4*(1+a*x)^9+3//4*a^-1*c^4*(1+a*x)^8+4//3*a^-1*c^4*(1+a*x)^6)
@test integrate(x^4*(c+-1*c*a^2*x^2)^-1*exp(2*arctanh(a*x)), x) == :(a^-5*c^-1*(1+-1*a*x)^-1+a^-3*c^-1*x^2+3*x*a^-4*c^-1+4*a^-5*c^-1*log(1+-1*a*x)+1//3*a^-2*c^-1*x^3)
@test integrate(x^3*(c+-1*c*a^2*x^2)^-1*exp(2*arctanh(a*x)), x) == :(a^-4*c^-1*(1+-1*a*x)^-1+(1/2)*a^-2*c^-1*x^2+2*x*a^-3*c^-1+3*a^-4*c^-1*log(1+-1*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-1*exp(2*arctanh(a*x)), x) == :(x*a^-2*c^-1+a^-3*c^-1*(1+-1*a*x)^-1+2*a^-3*c^-1*log(1+-1*a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-1*exp(2*arctanh(a*x)), x) == :(a^-2*c^-1*(1+-1*a*x)^-1+a^-2*c^-1*log(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^-1*exp(2*arctanh(a*x)), x) == :(a^-1*c^-1*(1+-1*a*x)^-1)
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-1*exp(2*arctanh(a*x)), x) == :(c^-1*(1+-1*a*x)^-1+c^-1*log(x)+-1*c^-1*log(1+-1*a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-1*exp(2*arctanh(a*x)), x) == :(-1*c^-1*x^-1+a*c^-1*(1+-1*a*x)^-1+-2*a*c^-1*log(1+-1*a*x)+2*a*c^-1*log(x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-1*exp(2*arctanh(a*x)), x) == :(-1//2*c^-1*x^-2+a^2*c^-1*(1+-1*a*x)^-1+-3*a^2*c^-1*log(1+-1*a*x)+-2*a*c^-1*x^-1+3*a^2*c^-1*log(x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^-1*exp(2*arctanh(a*x)), x) == :(-1//3*c^-1*x^-3+a^3*c^-1*(1+-1*a*x)^-1+-1*a*c^-1*x^-2+-4*a^3*c^-1*log(1+-1*a*x)+-3*a^2*c^-1*x^-1+4*a^3*c^-1*log(x))
@test integrate(x^4*(c+-1*c*a^2*x^2)^-2*exp(2*arctanh(a*x)), x) == :(-1*x*a^-4*c^-2+-17//8*a^-5*c^-2*log(1+-1*a*x)+-7//4*a^-5*c^-2*(1+-1*a*x)^-1+1//4*a^-5*c^-2*(1+-1*a*x)^-2+1//8*a^-5*c^-2*log(1+a*x))
@test integrate(x^3*(c+-1*c*a^2*x^2)^-2*exp(2*arctanh(a*x)), x) == :(-7//8*a^-4*c^-2*log(1+-1*a*x)+-5//4*a^-4*c^-2*(1+-1*a*x)^-1+-1//8*a^-4*c^-2*log(1+a*x)+1//4*a^-4*c^-2*(1+-1*a*x)^-2)
@test integrate(x^2*(c+-1*c*a^2*x^2)^-2*exp(2*arctanh(a*x)), x) == :(-3//4*a^-3*c^-2*(1+-1*a*x)^-1+1//4*a^-3*c^-2*(1+-1*a*x)^-2+1//4*a^-3*c^-2*arctanh(a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-2*exp(2*arctanh(a*x)), x) == :(-1//4*a^-2*c^-2*(1+-1*a*x)^-1+-1//4*a^-2*c^-2*arctanh(a*x)+1//4*a^-2*c^-2*(1+-1*a*x)^-2)
@test integrate((c+-1*c*a^2*x^2)^-2*exp(2*arctanh(a*x)), x) == :(1//4*a^-1*c^-2*(1+-1*a*x)^-1+1//4*a^-1*c^-2*(1+-1*a*x)^-2+1//4*a^-1*c^-2*arctanh(a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-2*exp(2*arctanh(a*x)), x) == :(c^-2*log(x)+-7//8*c^-2*log(1+-1*a*x)+-1//8*c^-2*log(1+a*x)+1//4*c^-2*(1+-1*a*x)^-2+3//4*c^-2*(1+-1*a*x)^-1)
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-2*exp(2*arctanh(a*x)), x) == :(-1*c^-2*x^-1+2*a*c^-2*log(x)+-17//8*a*c^-2*log(1+-1*a*x)+1//4*a*c^-2*(1+-1*a*x)^-2+1//8*a*c^-2*log(1+a*x)+5//4*a*c^-2*(1+-1*a*x)^-1)
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-2*exp(2*arctanh(a*x)), x) == :(-1//2*c^-2*x^-2+-2*a*c^-2*x^-1+4*a^2*c^-2*log(x)+-31//8*a^2*c^-2*log(1+-1*a*x)+-1//8*a^2*c^-2*log(1+a*x)+1//4*a^2*c^-2*(1+-1*a*x)^-2+7//4*a^2*c^-2*(1+-1*a*x)^-1)
@test integrate(x^-4*(c+-1*c*a^2*x^2)^-2*exp(2*arctanh(a*x)), x) == :(-1//3*c^-2*x^-3+-1*a*c^-2*x^-2+-4*a^2*c^-2*x^-1+6*a^3*c^-2*log(x)+-49//8*a^3*c^-2*log(1+-1*a*x)+1//4*a^3*c^-2*(1+-1*a*x)^-2+1//8*a^3*c^-2*log(1+a*x)+9//4*a^3*c^-2*(1+-1*a*x)^-1)
@test integrate(x^5*(c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(-1//2*a^-6*c^-3*(1+-1*a*x)^-2+1//12*a^-6*c^-3*(1+-1*a*x)^-3+1//16*a^-6*c^-3*(1+a*x)^-1+3//16*a^-6*c^-3*log(1+a*x)+13//16*a^-6*c^-3*log(1+-1*a*x)+23//16*a^-6*c^-3*(1+-1*a*x)^-1)
@test integrate(x^4*(c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(-3//8*a^-5*c^-3*(1+-1*a*x)^-2+-1//4*a^-5*c^-3*arctanh(a*x)+-1//16*a^-5*c^-3*(1+a*x)^-1+1//12*a^-5*c^-3*(1+-1*a*x)^-3+11//16*a^-5*c^-3*(1+-1*a*x)^-1)
@test integrate(x^3*(c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(-1//4*a^-4*c^-3*(1+-1*a*x)^-2+1//8*a^-4*c^-3*arctanh(a*x)+1//12*a^-4*c^-3*(1+-1*a*x)^-3+1//16*a^-4*c^-3*(1+a*x)^-1+3//16*a^-4*c^-3*(1+-1*a*x)^-1)
@test integrate(x^2*(c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(-1//6*a^-3*c^-3*(1+a*x)^-1*(1+-1*a*x)^-3*(1+-2*a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(-1//8*a^-2*c^-3*arctanh(a*x)+-1//16*a^-2*c^-3*(1+-1*a*x)^-1+1//12*a^-2*c^-3*(1+-1*a*x)^-3+1//16*a^-2*c^-3*(1+a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(-1//16*a^-1*c^-3*(1+a*x)^-1+1//4*a^-1*c^-3*arctanh(a*x)+1//8*a^-1*c^-3*(1+-1*a*x)^-2+1//12*a^-1*c^-3*(1+-1*a*x)^-3+3//16*a^-1*c^-3*(1+-1*a*x)^-1)
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(c^-3*log(x)+-13//16*c^-3*log(1+-1*a*x)+-3//16*c^-3*log(1+a*x)+1//4*c^-3*(1+-1*a*x)^-2+1//12*c^-3*(1+-1*a*x)^-3+1//16*c^-3*(1+a*x)^-1+11//16*c^-3*(1+-1*a*x)^-1)
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(-1*c^-3*x^-1+2*a*c^-3*log(x)+-9//4*a*c^-3*log(1+-1*a*x)+-1//16*a*c^-3*(1+a*x)^-1+1//4*a*c^-3*log(1+a*x)+1//12*a*c^-3*(1+-1*a*x)^-3+3//8*a*c^-3*(1+-1*a*x)^-2+23//16*a*c^-3*(1+-1*a*x)^-1)
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(-1//2*c^-3*x^-2+(1/2)*a^2*c^-3*(1+-1*a*x)^-2+-2*a*c^-3*x^-1+5*a^2*c^-3*log(x)+-75//16*a^2*c^-3*log(1+-1*a*x)+-5//16*a^2*c^-3*log(1+a*x)+1//12*a^2*c^-3*(1+-1*a*x)^-3+1//16*a^2*c^-3*(1+a*x)^-1+39//16*a^2*c^-3*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^-4*exp(2*arctanh(a*x)), x) == :(-5//64*a^-1*c^-4*(1+a*x)^-1+-1//64*a^-1*c^-4*(1+a*x)^-2+1//16*a^-1*c^-4*(1+-1*a*x)^-3+1//32*a^-1*c^-4*(1+-1*a*x)^-4+3//32*a^-1*c^-4*(1+-1*a*x)^-2+5//32*a^-1*c^-4*(1+-1*a*x)^-1+15//64*a^-1*c^-4*arctanh(a*x))
@test integrate(x^3*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//5*x^4*(c+-1*c*a^2*x^2)^(1/2)+-3//5*a^-2*x^2*(c+-1*c*a^2*x^2)^(1/2)+-1//2*a^-1*x^3*(c+-1*c*a^2*x^2)^(1/2)+-1//20*a^-4*(c+-1*c*a^2*x^2)^(1/2)*(24+15*a*x)+3//4*a^-4*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//4*x^3*(c+-1*c*a^2*x^2)^(1/2)+-2//3*a^-1*x^2*(c+-1*c*a^2*x^2)^(1/2)+-1//24*a^-3*(c+-1*c*a^2*x^2)^(1/2)*(32+21*a*x)+7//8*a^-3*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//3*x^2*(c+-1*c*a^2*x^2)^(1/2)+a^-2*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1//3*a^-2*(c+-1*c*a^2*x^2)^(1/2)*(5+3*a*x))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-3//2*a^-1*(c+-1*c*a^2*x^2)^(1/2)+-1//2*a^-1*(c+-1*c*a^2*x^2)^(1/2)*(1+a*x)+3//2*a^-1*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*(c+-1*c*a^2*x^2)^(1/2)+-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+2*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1*x^-1*(c+-1*c*a^2*x^2)^(1/2)+a*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-2*a*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//2*x^-2*(c+-1*c*a^2*x^2)^(1/2)+-2*a*x^-1*(c+-1*c*a^2*x^2)^(1/2)+-3//2*a^2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//3*x^-3*(c+-1*c*a^2*x^2)^(1/2)+-1*a*x^-2*(c+-1*c*a^2*x^2)^(1/2)+-1*a^3*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-5//3*a^2*x^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arctanh(a*x)), x) == :(-1//4*x^-4*(c+-1*c*a^2*x^2)^(1/2)+-7//8*a^2*x^-2*(c+-1*c*a^2*x^2)^(1/2)+-7//8*a^4*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-4//3*a^3*x^-1*(c+-1*c*a^2*x^2)^(1/2)+-2//3*a*x^-3*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^3*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//7*x^4*(c+-1*c*a^2*x^2)^3//2+-11//35*a^-2*x^2*(c+-1*c*a^2*x^2)^3//2+-1//3*a^-1*x^3*(c+-1*c*a^2*x^2)^3//2+-1//420*a^-4*(c+-1*c*a^2*x^2)^3//2*(88+105*a*x)+1//8*a^-4*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//8*c*x*a^-3*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^2*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//6*x^3*(c+-1*c*a^2*x^2)^3//2+-2//5*a^-1*x^2*(c+-1*c*a^2*x^2)^3//2+-1//120*a^-3*(c+-1*c*a^2*x^2)^3//2*(32+45*a*x)+3//16*a^-3*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+3//16*c*x*a^-2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//5*x^2*(c+-1*c*a^2*x^2)^3//2+-1//30*a^-2*(c+-1*c*a^2*x^2)^3//2*(14+15*a*x)+1//4*a^-2*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//4*c*x*a^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-5//12*a^-1*(c+-1*c*a^2*x^2)^3//2+-1//4*a^-1*(c+-1*c*a^2*x^2)^3//2*(1+a*x)+5//8*c*x*(c+-1*c*a^2*x^2)^(1/2)+5//8*a^-1*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//3*(c+-1*c*a^2*x^2)^3//2+c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1*c^3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+c*(c+-1*c*a^2*x^2)^(1/2)*(1+a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1*x^-1*(c+-1*c*a^2*x^2)^3//2+-2*a*c^3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-1//2*a*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+(1/2)*a*c*(c+-1*c*a^2*x^2)^(1/2)*(4+-1*a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//2*x^-2*(c+-1*c*a^2*x^2)^3//2+-2*a^2*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1//2*a^2*c^3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-1//2*a*c*x^-1*(c+-1*c*a^2*x^2)^(1/2)*(4+-1*a*x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//3*x^-3*(c+-1*c*a^2*x^2)^3//2+a^3*c^3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-1*a^3*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1*a*c*x^-2*(c+-1*c*a^2*x^2)^(1/2)*(1+a*x))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//4*x^-4*(c+-1*c*a^2*x^2)^3//2+-2//3*a*x^-3*(c+-1*c*a^2*x^2)^3//2+5//8*a^4*c^3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-5//8*c*a^2*x^-2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-6*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//5*x^-5*(c+-1*c*a^2*x^2)^3//2+-7//15*a^2*x^-3*(c+-1*c*a^2*x^2)^3//2+-1//2*a*x^-4*(c+-1*c*a^2*x^2)^3//2+1//4*a^5*c^3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-1//4*c*a^3*x^-2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-7*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//6*x^-6*(c+-1*c*a^2*x^2)^3//2+-4//15*a^3*x^-3*(c+-1*c*a^2*x^2)^3//2+-3//8*a^2*x^-4*(c+-1*c*a^2*x^2)^3//2+-2//5*a*x^-5*(c+-1*c*a^2*x^2)^3//2+3//16*a^6*c^3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-3//16*c*a^4*x^-2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-8*(c+-1*c*a^2*x^2)^3//2*exp(2*arctanh(a*x)), x) == :(-1//7*x^-7*(c+-1*c*a^2*x^2)^3//2+-22//105*a^4*x^-3*(c+-1*c*a^2*x^2)^3//2+-11//35*a^2*x^-5*(c+-1*c*a^2*x^2)^3//2+-1//3*a*x^-6*(c+-1*c*a^2*x^2)^3//2+-1//4*a^3*x^-4*(c+-1*c*a^2*x^2)^3//2+1//8*a^7*c^3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-1//8*c*a^5*x^-2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^3*(c+-1*c*a^2*x^2)^5//2*exp(2*arctanh(a*x)), x) == :(-1//9*x^4*(c+-1*c*a^2*x^2)^5//2+-13//63*a^-2*x^2*(c+-1*c*a^2*x^2)^5//2+-1//4*a^-1*x^3*(c+-1*c*a^2*x^2)^5//2+-1//2520*a^-4*(c+-1*c*a^2*x^2)^5//2*(208+315*a*x)+3//64*a^-4*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//32*c*x*a^-3*(c+-1*c*a^2*x^2)^3//2+3//64*x*a^-3*c^2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^2*(c+-1*c*a^2*x^2)^5//2*exp(2*arctanh(a*x)), x) == :(-1//8*x^3*(c+-1*c*a^2*x^2)^5//2+-2//7*a^-1*x^2*(c+-1*c*a^2*x^2)^5//2+-1//1680*a^-3*(c+-1*c*a^2*x^2)^5//2*(192+385*a*x)+11//128*a^-3*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+11//128*x*a^-2*c^2*(c+-1*c*a^2*x^2)^(1/2)+11//192*c*x*a^-2*(c+-1*c*a^2*x^2)^3//2)
@test integrate(x*(c+-1*c*a^2*x^2)^5//2*exp(2*arctanh(a*x)), x) == :(-1//7*x^2*(c+-1*c*a^2*x^2)^5//2+-1//105*a^-2*(c+-1*c*a^2*x^2)^5//2*(27+35*a*x)+1//8*a^-2*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//8*x*a^-1*c^2*(c+-1*c*a^2*x^2)^(1/2)+1//12*c*x*a^-1*(c+-1*c*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(2*arctanh(a*x)), x) == :(-7//30*a^-1*(c+-1*c*a^2*x^2)^5//2+-1//6*a^-1*(c+-1*c*a^2*x^2)^5//2*(1+a*x)+7//16*x*c^2*(c+-1*c*a^2*x^2)^(1/2)+7//16*a^-1*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+7//24*c*x*(c+-1*c*a^2*x^2)^3//2)
@test integrate(x^-1*(c+-1*c*a^2*x^2)^5//2*exp(2*arctanh(a*x)), x) == :(-1//5*(c+-1*c*a^2*x^2)^5//2+-1*c^5//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+3//4*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//4*c^2*(c+-1*c*a^2*x^2)^(1/2)*(4+3*a*x)+1//6*c*(c+-1*c*a^2*x^2)^3//2*(2+3*a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^5//2*exp(2*arctanh(a*x)), x) == :(-1*x^-1*(c+-1*c*a^2*x^2)^5//2+-2*a*c^5//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-9//8*a*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//8*a*c^2*(c+-1*c*a^2*x^2)^(1/2)*(16+-9*a*x)+1//12*a*c*(c+-1*c*a^2*x^2)^3//2*(8+-9*a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^5//2*exp(2*arctanh(a*x)), x) == :(-1//2*x^-2*(c+-1*c*a^2*x^2)^5//2+(1/2)*a^2*c^5//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-3*a^2*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1//2*a^2*c^2*(c+-1*c*a^2*x^2)^(1/2)*(1+6*a*x)+-1//6*a*c*x^-1*(c+-1*c*a^2*x^2)^3//2*(12+a*x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^5//2*exp(2*arctanh(a*x)), x) == :(-1//3*x^-3*(c+-1*c*a^2*x^2)^5//2+3*a^3*c^5//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-1//2*a^3*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1//2*a^2*c^2*x^-1*(c+-1*c*a^2*x^2)^(1/2)*(1+6*a*x)+-1//6*a*c*x^-2*(c+-1*c*a^2*x^2)^3//2*(6+-1*a*x))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^5//2*exp(2*arctanh(a*x)), x) == :(-1//4*x^-4*(c+-1*c*a^2*x^2)^5//2+2*a^4*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+9//8*a^4*c^5//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-1//24*a*c*x^-3*(c+-1*c*a^2*x^2)^3//2*(16+9*a*x)+1//8*a^3*c^2*x^-1*(c+-1*c*a^2*x^2)^(1/2)*(16+-9*a*x))
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(2*arctanh(a*x)), x) == :(-9//56*a^-1*(c+-1*c*a^2*x^2)^7//2+-1//8*a^-1*(c+-1*c*a^2*x^2)^7//2*(1+a*x)+3//16*c*x*(c+-1*c*a^2*x^2)^5//2+15//64*x*c^2*(c+-1*c*a^2*x^2)^3//2+45//128*x*c^3*(c+-1*c*a^2*x^2)^(1/2)+45//128*a^-1*c^7//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^3*(c+-1*c*a^2*x^2)^-1//2*exp(2*arctanh(a*x)), x) == :(a^-4*(1+a*x)^2*(c+-1*c*a^2*x^2)^-1//2+-3*a^-4*c^-1//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+11//3*a^-4*c^-1*(c+-1*c*a^2*x^2)^(1/2)+x*a^-3*c^-1*(c+-1*c*a^2*x^2)^(1/2)+1//3*a^-2*c^-1*x^2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-1//2*exp(2*arctanh(a*x)), x) == :(a^-3*(1+a*x)^2*(c+-1*c*a^2*x^2)^-1//2+-5//2*a^-3*c^-1//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+(1/2)*a^-3*c^-1*(c+-1*c*a^2*x^2)^(1/2)*(6+a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-1//2*exp(2*arctanh(a*x)), x) == :(a^-2*(1+a*x)^2*(c+-1*c*a^2*x^2)^-1//2+-2*a^-2*c^-1//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+2*a^-2*c^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(2*arctanh(a*x)), x) == :(a^-1*(c+-1*c*a^2*x^2)^-1//2*(2+2*a*x)+-1*a^-1*c^-1//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-1//2*exp(2*arctanh(a*x)), x) == :((c+-1*c*a^2*x^2)^-1//2*(2+2*a*x)+-1*c^-1//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-1//2*exp(2*arctanh(a*x)), x) == :(-1*c^-1*x^-1*(c+-1*c*a^2*x^2)^(1/2)+-2*a*c^-1//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+2*a*(c+-1*c*a^2*x^2)^-1//2*(1+a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-1//2*exp(2*arctanh(a*x)), x) == :(2*a^2*(c+-1*c*a^2*x^2)^-1//2*(1+a*x)+-5//2*a^2*c^-1//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-1//2*c^-1*x^-2*(c+-1*c*a^2*x^2)^(1/2)+-2*a*c^-1*x^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^-1//2*exp(2*arctanh(a*x)), x) == :(-3*a^3*c^-1//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+2*a^3*(c+-1*c*a^2*x^2)^-1//2*(1+a*x)+-1//3*c^-1*x^-3*(c+-1*c*a^2*x^2)^(1/2)+-1*a*c^-1*x^-2*(c+-1*c*a^2*x^2)^(1/2)+-8//3*a^2*c^-1*x^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^3*(c+-1*c*a^2*x^2)^-3//2*exp(2*arctanh(a*x)), x) == :(-1*a^-4*c^-2*(c+-1*c*a^2*x^2)^(1/2)+2*a^-4*c^-3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//3*a^-4*(1+a*x)^2*(c+-1*c*a^2*x^2)^-3//2+-1//3*a^-4*c^-1*(c+-1*c*a^2*x^2)^-1//2*(8+8*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-3//2*exp(2*arctanh(a*x)), x) == :(a^-3*c^-3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//3*a^-3*(1+a*x)^2*(c+-1*c*a^2*x^2)^-3//2+-1//3*a^-3*c^-1*(c+-1*c*a^2*x^2)^-1//2*(5+5*a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-3//2*exp(2*arctanh(a*x)), x) == :(1//3*a^-2*(1+a*x)^2*(c+-1*c*a^2*x^2)^-3//2+-1//3*a^-2*c^-1*(c+-1*c*a^2*x^2)^-1//2*(2+2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(2*arctanh(a*x)), x) == :(1//3*x*c^-1*(c+-1*c*a^2*x^2)^-1//2+1//3*a^-1*(c+-1*c*a^2*x^2)^-3//2*(2+2*a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-3//2*exp(2*arctanh(a*x)), x) == :(-1*c^-3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+1//3*(c+-1*c*a^2*x^2)^-3//2*(2+2*a*x)+1//3*c^-1*(c+-1*c*a^2*x^2)^-1//2*(3+4*a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-3//2*exp(2*arctanh(a*x)), x) == :(-1*c^-2*x^-1*(c+-1*c*a^2*x^2)^(1/2)+-2*a*c^-3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+2//3*a*(c+-1*c*a^2*x^2)^-3//2*(1+a*x)+1//3*a*c^-1*(c+-1*c*a^2*x^2)^-1//2*(6+7*a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-3//2*exp(2*arctanh(a*x)), x) == :(-7//2*a^2*c^-3//2*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-1//2*c^-2*x^-2*(c+-1*c*a^2*x^2)^(1/2)+2//3*a^2*(c+-1*c*a^2*x^2)^-3//2*(1+a*x)+-2*a*c^-2*x^-1*(c+-1*c*a^2*x^2)^(1/2)+1//3*a^2*c^-1*(c+-1*c*a^2*x^2)^-1//2*(9+10*a*x))
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(2*arctanh(a*x)), x) == :(1//5*x*c^-1*(c+-1*c*a^2*x^2)^-3//2+1//5*a^-1*(c+-1*c*a^2*x^2)^-5//2*(2+2*a*x)+2//5*x*c^-2*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(2*arctanh(a*x)), x) == :(1//7*x*c^-1*(c+-1*c*a^2*x^2)^-5//2+1//7*a^-1*(c+-1*c*a^2*x^2)^-7//2*(2+2*a*x)+4//21*x*c^-2*(c+-1*c*a^2*x^2)^-3//2+8//21*x*c^-3*(c+-1*c*a^2*x^2)^-1//2)
@test integrate(x^m*(c+-1*c*a^2*x^2)^3*exp(2*arctanh(a*x)), x) == :(c^3*x^(1+m)*(1+m)^-1+a^6*c^3*x^(7+m)*(7+m)^-1+-1*a^2*c^3*x^(3+m)*(3+m)^-1+-1*a^4*c^3*x^(5+m)*(5+m)^-1+-4*a^3*c^3*x^(4+m)*(4+m)^-1+2*a*c^3*x^(2+m)*(2+m)^-1+2*a^5*c^3*x^(6+m)*(6+m)^-1)
@test integrate(x^m*(c+-1*c*a^2*x^2)^2*exp(2*arctanh(a*x)), x) == :(c^2*x^(1+m)*(1+m)^-1+-1*a^4*c^2*x^(5+m)*(5+m)^-1+-2*a^3*c^2*x^(4+m)*(4+m)^-1+2*a*c^2*x^(2+m)*(2+m)^-1)
@test integrate(x^m*(c+-1*c*a^2*x^2)*exp(2*arctanh(a*x)), x) == :(c*x^(1+m)*(1+m)^-1+c*a^2*x^(3+m)*(3+m)^-1+2*a*c*x^(2+m)*(2+m)^-1)
@test integrate(x^3*(c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(-3//5*c*x^4*(1+-1*a^2*x^2)^(1/2)+23//16*c*a^-4*arcsin(a*x)+-23//24*c*a^-1*x^3*(1+-1*a^2*x^2)^(1/2)+-17//15*c*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)+-1//6*a*c*x^5*(1+-1*a^2*x^2)^(1/2)+-1//240*c*a^-4*(1+-1*a^2*x^2)^(1/2)*(544+345*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(-3//4*c*x^3*(1+-1*a^2*x^2)^(1/2)+13//8*c*a^-3*arcsin(a*x)+-19//15*c*a^-1*x^2*(1+-1*a^2*x^2)^(1/2)+-1//5*a*c*x^4*(1+-1*a^2*x^2)^(1/2)+-1//120*c*a^-3*(1+-1*a^2*x^2)^(1/2)*(304+195*a*x))
@test integrate(x*(c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(-15//8*c*a^-2*(1+-1*a^2*x^2)^(1/2)+15//8*c*a^-2*arcsin(a*x)+-5//8*c*a^-2*(1+-1*a^2*x^2)^(1/2)*(1+a*x)+-1//4*c*a^-2*(1+a*x)^2*(1+-1*a^2*x^2)^(1/2)+-1//4*c*a^-2*(1+a*x)^3*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(-5//2*c*a^-1*(1+-1*a^2*x^2)^(1/2)+5//2*c*a^-1*arcsin(a*x)+-5//6*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(1+a*x)+-1//3*c*a^-1*(1+a*x)^2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(-1*c*arctanh((1+-1*a^2*x^2)^(1/2))+-3*c*(1+-1*a^2*x^2)^(1/2)+7//2*c*arcsin(a*x)+-1//2*a*c*x*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-2*(c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(-1*a*c*(1+-1*a^2*x^2)^(1/2)+-1*c*x^-1*(1+-1*a^2*x^2)^(1/2)+-3*a*c*arctanh((1+-1*a^2*x^2)^(1/2))+3*a*c*arcsin(a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(c*a^2*arcsin(a*x)+-7//2*c*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1//2*c*x^-2*(1+-1*a^2*x^2)^(1/2)+-3*a*c*x^-1*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-4*(c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(-5//2*c*a^3*arctanh((1+-1*a^2*x^2)^(1/2))+-1//3*c*x^-3*(1+-1*a^2*x^2)^(1/2)+-11//3*c*a^2*x^-1*(1+-1*a^2*x^2)^(1/2)+-3//2*a*c*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-5*(c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(-15//8*c*a^4*arctanh((1+-1*a^2*x^2)^(1/2))+-1//4*c*x^-4*(1+-1*a^2*x^2)^(1/2)+-1*a*c*x^-3*(1+-1*a^2*x^2)^(1/2)+-3*c*a^3*x^-1*(1+-1*a^2*x^2)^(1/2)+-15//8*c*a^2*x^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate(x^-6*(c+-1*c*a^2*x^2)*exp(3*arctanh(a*x)), x) == :(-13//8*c*a^5*arctanh((1+-1*a^2*x^2)^(1/2))+-1//5*c*x^-5*(1+-1*a^2*x^2)^(1/2)+-38//15*c*a^4*x^-1*(1+-1*a^2*x^2)^(1/2)+-19//15*c*a^2*x^-3*(1+-1*a^2*x^2)^(1/2)+-13//8*c*a^3*x^-2*(1+-1*a^2*x^2)^(1/2)+-3//4*a*c*x^-4*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^2*exp(3*arctanh(a*x)), x) == :(-7//12*a^-1*c^2*(1+-1*a^2*x^2)^3//2+7//8*x*c^2*(1+-1*a^2*x^2)^(1/2)+7//8*a^-1*c^2*arcsin(a*x)+-7//20*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(1+a*x)+-1//5*a^-1*c^2*(1+a*x)^2*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^3*exp(3*arctanh(a*x)), x) == :(-3//10*a^-1*c^3*(1+-1*a^2*x^2)^5//2+3//8*x*c^3*(1+-1*a^2*x^2)^3//2+9//16*x*c^3*(1+-1*a^2*x^2)^(1/2)+9//16*a^-1*c^3*arcsin(a*x)+-3//14*a^-1*c^3*(1+-1*a^2*x^2)^5//2*(1+a*x)+-1//7*a^-1*c^3*(1+a*x)^2*(1+-1*a^2*x^2)^5//2)
@test integrate((c+-1*c*a^2*x^2)^4*exp(3*arctanh(a*x)), x) == :(-11//56*a^-1*c^4*(1+-1*a^2*x^2)^7//2+11//48*x*c^4*(1+-1*a^2*x^2)^5//2+55//128*x*c^4*(1+-1*a^2*x^2)^(1/2)+55//128*a^-1*c^4*arcsin(a*x)+55//192*x*c^4*(1+-1*a^2*x^2)^3//2+-11//72*a^-1*c^4*(1+-1*a^2*x^2)^7//2*(1+a*x)+-1//9*a^-1*c^4*(1+a*x)^2*(1+-1*a^2*x^2)^7//2)
@test integrate(x^2*(c+-1*c*a^2*x^2)^-1*exp(3*arctanh(a*x)), x) == :(-3*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)+3*a^-3*c^-1*arcsin(a*x)+-2*a^-3*c^-1*(1+a*x)^2*(1+-1*a^2*x^2)^-1//2+1//3*a^-3*c^-1*(1+a*x)^3*(1+-1*a^2*x^2)^-3//2)
@test integrate(x*(c+-1*c*a^2*x^2)^-1*exp(3*arctanh(a*x)), x) == :(a^-2*c^-1*arcsin(a*x)+-1*a^-2*c^-1*(1+-1*a^2*x^2)^-1//2*(2+2*a*x)+1//3*a^-2*c^-1*(1+a*x)^3*(1+-1*a^2*x^2)^-3//2)
@test integrate((c+-1*c*a^2*x^2)^-1*exp(3*arctanh(a*x)), x) == :(1//3*a^-1*c^-1*exp(3*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(3*arctanh(a*x)), x) == :(1//5*a^-1*c^-2*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^(1/2)+2//15*a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)+2//15*a^-1*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(3*arctanh(a*x)), x) == :(8//35*x*c^-3*(1+-1*a^2*x^2)^-1//2+1//7*a^-1*c^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^-1//2+4//35*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^-1//2+4//35*a^-1*c^-3*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-4*exp(3*arctanh(a*x)), x) == :(8//63*x*c^-4*(1+-1*a^2*x^2)^-3//2+16//63*x*c^-4*(1+-1*a^2*x^2)^-1//2+1//9*a^-1*c^-4*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^-3//2+2//21*a^-1*c^-4*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^-3//2+2//21*a^-1*c^-4*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^-3//2)
@test integrate(x^3*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-3//4*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*x*a^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^-4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x)+-2*a^-2*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4//3*a^-1*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//5*a*x^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*x*a^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x)+-2*a^-1*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//4*a*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-3//2*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*x*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x)+-1//3*a*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-3*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x)+-1//2*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arctanh(a*x)), x) == :((1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+-4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x)+-1*a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x)+3*a*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1//2*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x)+-3*a*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1//3*x^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^2*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x)+4*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+-3//2*a*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arctanh(a*x)), x) == :(-1//4*x^-4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1*a*x^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^3*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x)+-2*a^2*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(3*arctanh(a*x)), x) == :(1//4*c*a^-1*(1+a*x)^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(3*arctanh(a*x)), x) == :(-1//6*a^-1*c^2*(1+a*x)^6*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+2//5*a^-1*c^2*(1+a*x)^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(3*arctanh(a*x)), x) == :(-4//7*a^-1*c^3*(1+a*x)^7*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//8*a^-1*c^3*(1+a*x)^8*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+2//3*a^-1*c^3*(1+a*x)^6*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^9//2*exp(3*arctanh(a*x)), x) == :(-3//2*a^-1*c^4*(1+a*x)^8*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//10*a^-1*c^4*(1+a*x)^10*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+2//3*a^-1*c^4*(1+a*x)^9*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+8//7*a^-1*c^4*(1+a*x)^7*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(3*arctanh(a*x)), x) == :(a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+2*a^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(3*arctanh(a*x)), x) == :((1/2)*a^-1*c^-1*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(3*arctanh(a*x)), x) == :(1//6*a^-1*c^-2*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-1*c^-2*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(3*arctanh(a*x)), x) == :(-1//32*a^-1*c^-3*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//12*a^-1*c^-3*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//16*a^-1*c^-3*(1+-1*a*x)^-4*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+3//32*a^-1*c^-3*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+5//32*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^5*exp(4*arctanh(a*x)), x) == :(a^-1*c^5*(1+a*x)^8+-4//3*a^-1*c^5*(1+a*x)^9+-1//11*a^-1*c^5*(1+a*x)^11+3//5*a^-1*c^5*(1+a*x)^10)
@test integrate((c+-1*c*a^2*x^2)^4*exp(4*arctanh(a*x)), x) == :(-1//2*a^-1*c^4*(1+a*x)^8+1//9*a^-1*c^4*(1+a*x)^9+4//7*a^-1*c^4*(1+a*x)^7)
@test integrate((c+-1*c*a^2*x^2)^3*exp(4*arctanh(a*x)), x) == :(-1//7*a^-1*c^3*(1+a*x)^7+1//3*a^-1*c^3*(1+a*x)^6)
@test integrate((c+-1*c*a^2*x^2)^2*exp(4*arctanh(a*x)), x) == :(1//5*a^-1*c^2*(1+a*x)^5)
@test integrate((c+-1*c*a^2*x^2)^-1*exp(4*arctanh(a*x)), x) == :(x*c^-1*(1+-1*a*x)^-2)
@test integrate((c+-1*c*a^2*x^2)^-2*exp(4*arctanh(a*x)), x) == :(1//3*a^-1*c^-2*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^2*x^2)^-3*exp(4*arctanh(a*x)), x) == :(1//8*a^-1*c^-3*(1+-1*a*x)^-4+1//12*a^-1*c^-3*(1+-1*a*x)^-3+1//16*a^-1*c^-3*(1+-1*a*x)^-1+1//16*a^-1*c^-3*(1+-1*a*x)^-2+1//16*a^-1*c^-3*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-4*exp(4*arctanh(a*x)), x) == :(-1//64*a^-1*c^-4*(1+a*x)^-1+1//16*a^-1*c^-4*(1+-1*a*x)^-4+1//16*a^-1*c^-4*(1+-1*a*x)^-3+1//16*a^-1*c^-4*(1+-1*a*x)^-2+1//20*a^-1*c^-4*(1+-1*a*x)^-5+3//32*a^-1*c^-4*arctanh(a*x)+5//64*a^-1*c^-4*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^4*exp(-1*arctanh(a*x)), x) == :(1//8*x*c^4*(1+-1*a^2*x^2)^7//2+1//9*a^-1*c^4*(1+-1*a^2*x^2)^9//2+7//48*x*c^4*(1+-1*a^2*x^2)^5//2+35//128*x*c^4*(1+-1*a^2*x^2)^(1/2)+35//128*a^-1*c^4*arcsin(a*x)+35//192*x*c^4*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^3*exp(-1*arctanh(a*x)), x) == :(1//6*x*c^3*(1+-1*a^2*x^2)^5//2+1//7*a^-1*c^3*(1+-1*a^2*x^2)^7//2+5//16*x*c^3*(1+-1*a^2*x^2)^(1/2)+5//16*a^-1*c^3*arcsin(a*x)+5//24*x*c^3*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^2*exp(-1*arctanh(a*x)), x) == :(1//4*x*c^2*(1+-1*a^2*x^2)^3//2+1//5*a^-1*c^2*(1+-1*a^2*x^2)^5//2+3//8*x*c^2*(1+-1*a^2*x^2)^(1/2)+3//8*a^-1*c^2*arcsin(a*x))
@test integrate((c+-1*c*a^2*x^2)*exp(-1*arctanh(a*x)), x) == :((1/2)*c*x*(1+-1*a^2*x^2)^(1/2)+(1/2)*c*a^-1*arcsin(a*x)+1//3*c*a^-1*(1+-1*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^-1*exp(-1*arctanh(a*x)), x) == :(-1*a^-1*c^-1*exp(-1*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(-1*arctanh(a*x)), x) == :(2//3*x*c^-2*(1+-1*a^2*x^2)^-1//2+-1//3*a^-1*c^-2*(1+-1*a^2*x^2)^-3//2*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(-1*arctanh(a*x)), x) == :(4//15*x*c^-3*(1+-1*a^2*x^2)^-3//2+8//15*x*c^-3*(1+-1*a^2*x^2)^-1//2+-1//5*a^-1*c^-3*(1+-1*a^2*x^2)^-5//2*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^-4*exp(-1*arctanh(a*x)), x) == :(6//35*x*c^-4*(1+-1*a^2*x^2)^-5//2+8//35*x*c^-4*(1+-1*a^2*x^2)^-3//2+16//35*x*c^-4*(1+-1*a^2*x^2)^-1//2+-1//7*a^-1*c^-4*(1+-1*a^2*x^2)^-7//2*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^-5*exp(-1*arctanh(a*x)), x) == :(8//63*x*c^-5*(1+-1*a^2*x^2)^-7//2+16//105*x*c^-5*(1+-1*a^2*x^2)^-5//2+64//315*x*c^-5*(1+-1*a^2*x^2)^-3//2+128//315*x*c^-5*(1+-1*a^2*x^2)^-1//2+-1//9*a^-1*c^-5*(1+-1*a^2*x^2)^-9//2*(1+-1*a*x))
@test integrate(x^m*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(x^(1+m)*(1+m)^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1*a*x^(2+m)*(1+-1*a^2*x^2)^-1//2*(2+m)^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(1//3*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//4*a*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arctanh(a*x)), x) == :((1/2)*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//3*a*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//2*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arctanh(a*x)), x) == :((1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+-1*a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arctanh(a*x)), x) == :(-1*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1*a*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(-1*arctanh(a*x)), x) == :(-2//3*c*a^-1*(1+-1*a*x)^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//4*c*a^-1*(1+-1*a*x)^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(-1*arctanh(a*x)), x) == :(-1*a^-1*c^2*(1+-1*a*x)^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//6*a^-1*c^2*(1+-1*a*x)^6*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4//5*a^-1*c^2*(1+-1*a*x)^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(-1*arctanh(a*x)), x) == :(2*a^-1*c^3*(1+-1*a*x)^6*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-8//5*a^-1*c^3*(1+-1*a*x)^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-6//7*a^-1*c^3*(1+-1*a*x)^7*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//8*a^-1*c^3*(1+-1*a*x)^8*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^9//2*exp(-1*arctanh(a*x)), x) == :(-3*a^-1*c^4*(1+-1*a*x)^8*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-8//3*a^-1*c^4*(1+-1*a*x)^6*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//10*a^-1*c^4*(1+-1*a*x)^10*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+8//9*a^-1*c^4*(1+-1*a*x)^9*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+32//7*a^-1*c^4*(1+-1*a*x)^7*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(-1*arctanh(a*x)), x) == :(a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(-1*arctanh(a*x)), x) == :((1/2)*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x)+-1//2*a^-1*c^-1*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(-1*arctanh(a*x)), x) == :(-1//4*a^-1*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//8*a^-1*c^-2*(1+a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+3//8*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(-1*arctanh(a*x)), x) == :(-3//16*a^-1*c^-3*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-3//32*a^-1*c^-3*(1+a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//24*a^-1*c^-3*(1+a*x)^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//32*a^-1*c^-3*(1+-1*a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+5//16*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^4*exp(-2*arctanh(a*x)), x) == :(-4//3*a^-1*c^4*(1+-1*a*x)^6+-3//4*a^-1*c^4*(1+-1*a*x)^8+1//9*a^-1*c^4*(1+-1*a*x)^9+12//7*a^-1*c^4*(1+-1*a*x)^7)
@test integrate((c+-1*c*a^2*x^2)^3*exp(-2*arctanh(a*x)), x) == :(-4//5*a^-1*c^3*(1+-1*a*x)^5+-1//7*a^-1*c^3*(1+-1*a*x)^7+2//3*a^-1*c^3*(1+-1*a*x)^6)
@test integrate((c+-1*c*a^2*x^2)^2*exp(-2*arctanh(a*x)), x) == :(-1//2*a^-1*c^2*(1+-1*a*x)^4+1//5*a^-1*c^2*(1+-1*a*x)^5)
@test integrate((c+-1*c*a^2*x^2)*exp(-2*arctanh(a*x)), x) == :(-1//3*c*a^-1*(1+-1*a*x)^3)
@test integrate((c+-1*c*a^2*x^2)^-1*exp(-2*arctanh(a*x)), x) == :(-1*a^-1*c^-1*(1+a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^-2*exp(-2*arctanh(a*x)), x) == :(-1//4*a^-1*c^-2*(1+a*x)^-1+-1//4*a^-1*c^-2*(1+a*x)^-2+1//4*a^-1*c^-2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(-2*arctanh(a*x)), x) == :(-3//16*a^-1*c^-3*(1+a*x)^-1+-1//8*a^-1*c^-3*(1+a*x)^-2+-1//12*a^-1*c^-3*(1+a*x)^-3+1//4*a^-1*c^-3*arctanh(a*x)+1//16*a^-1*c^-3*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^-4*exp(-2*arctanh(a*x)), x) == :(-5//32*a^-1*c^-4*(1+a*x)^-1+-3//32*a^-1*c^-4*(1+a*x)^-2+-1//16*a^-1*c^-4*(1+a*x)^-3+-1//32*a^-1*c^-4*(1+a*x)^-4+1//64*a^-1*c^-4*(1+-1*a*x)^-2+5//64*a^-1*c^-4*(1+-1*a*x)^-1+15//64*a^-1*c^-4*arctanh(a*x))
@test integrate(x^3*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//5*x^4*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*a^-1*x^3*(c+-1*c*a^2*x^2)^(1/2)+-3//4*a^-4*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-3//5*a^-2*x^2*(c+-1*c*a^2*x^2)^(1/2)+-1//20*a^-4*(c+-1*c*a^2*x^2)^(1/2)*(24+-15*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//4*x^3*(c+-1*c*a^2*x^2)^(1/2)+1//24*a^-3*(c+-1*c*a^2*x^2)^(1/2)*(32+-21*a*x)+2//3*a^-1*x^2*(c+-1*c*a^2*x^2)^(1/2)+7//8*a^-3*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//3*x^2*(c+-1*c*a^2*x^2)^(1/2)+-1*a^-2*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1//3*a^-2*(c+-1*c*a^2*x^2)^(1/2)*(5+-3*a*x))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(3//2*a^-1*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*a^-1*(c+-1*c*a^2*x^2)^(1/2)*(1+-1*a*x)+3//2*a^-1*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*(c+-1*c*a^2*x^2)^(1/2)+-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-2*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1*x^-1*(c+-1*c*a^2*x^2)^(1/2)+a*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+2*a*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//2*x^-2*(c+-1*c*a^2*x^2)^(1/2)+2*a*x^-1*(c+-1*c*a^2*x^2)^(1/2)+-3//2*a^2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//3*x^-3*(c+-1*c*a^2*x^2)^(1/2)+a*x^-2*(c+-1*c*a^2*x^2)^(1/2)+a^3*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-5//3*a^2*x^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arctanh(a*x)), x) == :(-1//4*x^-4*(c+-1*c*a^2*x^2)^(1/2)+-7//8*a^2*x^-2*(c+-1*c*a^2*x^2)^(1/2)+-7//8*a^4*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+2//3*a*x^-3*(c+-1*c*a^2*x^2)^(1/2)+4//3*a^3*x^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(-2*arctanh(a*x)), x) == :(5//12*a^-1*(c+-1*c*a^2*x^2)^3//2+1//4*a^-1*(c+-1*c*a^2*x^2)^3//2*(1+-1*a*x)+5//8*c*x*(c+-1*c*a^2*x^2)^(1/2)+5//8*a^-1*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(-2*arctanh(a*x)), x) == :(7//30*a^-1*(c+-1*c*a^2*x^2)^5//2+1//6*a^-1*(c+-1*c*a^2*x^2)^5//2*(1+-1*a*x)+7//16*x*c^2*(c+-1*c*a^2*x^2)^(1/2)+7//16*a^-1*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+7//24*c*x*(c+-1*c*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(-2*arctanh(a*x)), x) == :(9//56*a^-1*(c+-1*c*a^2*x^2)^7//2+1//8*a^-1*(c+-1*c*a^2*x^2)^7//2*(1+-1*a*x)+3//16*c*x*(c+-1*c*a^2*x^2)^5//2+15//64*x*c^2*(c+-1*c*a^2*x^2)^3//2+45//128*x*c^3*(c+-1*c*a^2*x^2)^(1/2)+45//128*a^-1*c^7//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(-2*arctanh(a*x)), x) == :(-1*a^-1*c^-1//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1*a^-1*(c+-1*c*a^2*x^2)^-1//2*(2+-2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(-2*arctanh(a*x)), x) == :(-1//3*a^-1*(c+-1*c*a^2*x^2)^-3//2*(2+-2*a*x)+1//3*x*c^-1*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(-2*arctanh(a*x)), x) == :(-1//5*a^-1*(c+-1*c*a^2*x^2)^-5//2*(2+-2*a*x)+1//5*x*c^-1*(c+-1*c*a^2*x^2)^-3//2+2//5*x*c^-2*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(-2*arctanh(a*x)), x) == :(-1//7*a^-1*(c+-1*c*a^2*x^2)^-7//2*(2+-2*a*x)+1//7*x*c^-1*(c+-1*c*a^2*x^2)^-5//2+4//21*x*c^-2*(c+-1*c*a^2*x^2)^-3//2+8//21*x*c^-3*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^4*exp(-3*arctanh(a*x)), x) == :(11//48*x*c^4*(1+-1*a^2*x^2)^5//2+11//56*a^-1*c^4*(1+-1*a^2*x^2)^7//2+55//128*x*c^4*(1+-1*a^2*x^2)^(1/2)+55//128*a^-1*c^4*arcsin(a*x)+55//192*x*c^4*(1+-1*a^2*x^2)^3//2+1//9*a^-1*c^4*(1+-1*a*x)^2*(1+-1*a^2*x^2)^7//2+11//72*a^-1*c^4*(1+-1*a^2*x^2)^7//2*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^3*exp(-3*arctanh(a*x)), x) == :(3//8*x*c^3*(1+-1*a^2*x^2)^3//2+3//10*a^-1*c^3*(1+-1*a^2*x^2)^5//2+9//16*x*c^3*(1+-1*a^2*x^2)^(1/2)+9//16*a^-1*c^3*arcsin(a*x)+1//7*a^-1*c^3*(1+-1*a*x)^2*(1+-1*a^2*x^2)^5//2+3//14*a^-1*c^3*(1+-1*a^2*x^2)^5//2*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^2*exp(-3*arctanh(a*x)), x) == :(7//8*x*c^2*(1+-1*a^2*x^2)^(1/2)+7//8*a^-1*c^2*arcsin(a*x)+7//12*a^-1*c^2*(1+-1*a^2*x^2)^3//2+1//5*a^-1*c^2*(1+-1*a*x)^2*(1+-1*a^2*x^2)^3//2+7//20*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)*exp(-3*arctanh(a*x)), x) == :(5//2*c*a^-1*(1+-1*a^2*x^2)^(1/2)+5//2*c*a^-1*arcsin(a*x)+1//3*c*a^-1*(1+-1*a*x)^2*(1+-1*a^2*x^2)^(1/2)+5//6*c*a^-1*(1+-1*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^-1*exp(-3*arctanh(a*x)), x) == :(-1//3*a^-1*c^-1*exp(-3*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(-3*arctanh(a*x)), x) == :(-2//15*a^-1*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)+-2//15*a^-1*c^-2*(1+a*x)^-2*(1+-1*a^2*x^2)^(1/2)+-1//5*a^-1*c^-2*(1+a*x)^-3*(1+-1*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(-3*arctanh(a*x)), x) == :(8//35*x*c^-3*(1+-1*a^2*x^2)^-1//2+-4//35*a^-1*c^-3*(1+a*x)^-1*(1+-1*a^2*x^2)^-1//2+-4//35*a^-1*c^-3*(1+a*x)^-2*(1+-1*a^2*x^2)^-1//2+-1//7*a^-1*c^-3*(1+a*x)^-3*(1+-1*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-4*exp(-3*arctanh(a*x)), x) == :(8//63*x*c^-4*(1+-1*a^2*x^2)^-3//2+16//63*x*c^-4*(1+-1*a^2*x^2)^-1//2+-2//21*a^-1*c^-4*(1+a*x)^-1*(1+-1*a^2*x^2)^-3//2+-2//21*a^-1*c^-4*(1+a*x)^-2*(1+-1*a^2*x^2)^-3//2+-1//9*a^-1*c^-4*(1+a*x)^-3*(1+-1*a^2*x^2)^-3//2)
@test integrate(x^3*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-3//4*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^-4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x)+-2*a^-2*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*x*a^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//5*a*x^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4//3*a^-1*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*x*a^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+2*a^-1*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x)+1//4*a*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-3//2*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x)+4*x*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//3*a*x^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-3*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arctanh(a*x)), x) == :((1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+-4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x)+a*x*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-3*a*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+4*a*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1//2*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x)+3*a*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1//3*x^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^2*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+4*a^3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x)+3//2*a*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arctanh(a*x)), x) == :(-1//4*x^-4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+a*x^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x)+-2*a^2*x^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^3*x^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate((c+-1*c*a^2*x^2)^9//2*exp(-3*arctanh(a*x)), x) == :(-8//7*a^-1*c^4*(1+-1*a*x)^7*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-2//3*a^-1*c^4*(1+-1*a*x)^9*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//10*a^-1*c^4*(1+-1*a*x)^10*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+3//2*a^-1*c^4*(1+-1*a*x)^8*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(-3*arctanh(a*x)), x) == :(-2//3*a^-1*c^3*(1+-1*a*x)^6*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//8*a^-1*c^3*(1+-1*a*x)^8*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4//7*a^-1*c^3*(1+-1*a*x)^7*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(-3*arctanh(a*x)), x) == :(-2//5*a^-1*c^2*(1+-1*a*x)^5*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//6*a^-1*c^2*(1+-1*a*x)^6*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(-3*arctanh(a*x)), x) == :(-1//4*c*a^-1*(1+-1*a*x)^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(-3*arctanh(a*x)), x) == :(-1*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+-2*a^-1*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(-3*arctanh(a*x)), x) == :(-1//2*a^-1*c^-1*(1+a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(-3*arctanh(a*x)), x) == :(-1//6*a^-1*c^-2*(1+a*x)^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//8*a^-1*c^-2*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//8*a^-1*c^-2*(1+a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//8*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(-3*arctanh(a*x)), x) == :(-3//32*a^-1*c^-3*(1+a*x)^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//8*a^-1*c^-3*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//12*a^-1*c^-3*(1+a*x)^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//16*a^-1*c^-3*(1+a*x)^-4*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//32*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+5//32*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctanh(a*x))
@test integrate((1+-1*a^2*x^2)^5//2*exp((1/2)*arctanh(a*x)), x) == :(-231//1024*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-231//2048*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-77//480*a^-1*(1+a*x)^3//4*(1+-1*a*x)^13//4+-11//60*a^-1*(1+a*x)^7//4*(1+-1*a*x)^13//4+-1//6*a^-1*(1+a*x)^11//4*(1+-1*a*x)^13//4+77//960*a^-1*(1+a*x)^3//4*(1+-1*a*x)^9//4+231//512*a^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4+231//1024*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+231//1280*a^-1*(1+a*x)^3//4*(1+-1*a*x)^5//4+231//2048*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((1+-1*a^2*x^2)^3//2*exp((1/2)*arctanh(a*x)), x) == :(-35//128*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-35//256*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-7//24*a^-1*(1+a*x)^3//4*(1+-1*a*x)^9//4+-1//4*a^-1*(1+a*x)^7//4*(1+-1*a*x)^9//4+7//32*a^-1*(1+a*x)^3//4*(1+-1*a*x)^5//4+35//64*a^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4+35//128*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+35//256*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((1+-1*a^2*x^2)^(1/2)*exp((1/2)*arctanh(a*x)), x) == :(-3//8*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-3//16*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*a^-1*(1+a*x)^3//4*(1+-1*a*x)^5//4+3//4*a^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4+3//8*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+3//16*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((1+-1*a^2*x^2)^-1//2*exp((1/2)*arctanh(a*x)), x) == :(2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*2^(1/2)*a^-1*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((1+-1*a^2*x^2)^-3//2*exp((1/2)*arctanh(a*x)), x) == :(-2//3*a^-1*(1+-1*a^2*x^2)^-1//2*(1+-2*a*x)*exp((1/2)*arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-5//2*exp((1/2)*arctanh(a*x)), x) == :(-16//35*a^-1*(1+-1*a^2*x^2)^-1//2*(1+-2*a*x)*exp((1/2)*arctanh(a*x))+-2//35*a^-1*(1+-1*a^2*x^2)^-3//2*(1+-6*a*x)*exp((1/2)*arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-7//2*exp((1/2)*arctanh(a*x)), x) == :(-256//693*a^-1*(1+-1*a^2*x^2)^-1//2*(1+-2*a*x)*exp((1/2)*arctanh(a*x))+-32//693*a^-1*(1+-1*a^2*x^2)^-3//2*(1+-6*a*x)*exp((1/2)*arctanh(a*x))+-2//99*a^-1*(1+-1*a^2*x^2)^-5//2*(1+-10*a*x)*exp((1/2)*arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^-9//2*exp((1/2)*arctanh(a*x)), x) == :(-2048//6435*a^-1*(1+-1*a^2*x^2)^-1//2*(1+-2*a*x)*exp((1/2)*arctanh(a*x))+-256//6435*a^-1*(1+-1*a^2*x^2)^-3//2*(1+-6*a*x)*exp((1/2)*arctanh(a*x))+-112//6435*a^-1*(1+-1*a^2*x^2)^-5//2*(1+-10*a*x)*exp((1/2)*arctanh(a*x))+-2//195*a^-1*(1+-1*a^2*x^2)^-7//2*(1+-14*a*x)*exp((1/2)*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^5//2*exp((1/2)*arctanh(a*x)), x) == :(-231//1024*2^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-231//2048*2^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-77//480*a^-1*c^2*(1+a*x)^3//4*(1+-1*a*x)^13//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-11//60*a^-1*c^2*(1+a*x)^7//4*(1+-1*a*x)^13//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//6*a^-1*c^2*(1+a*x)^11//4*(1+-1*a*x)^13//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+77//960*a^-1*c^2*(1+a*x)^3//4*(1+-1*a*x)^9//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+231//512*a^-1*c^2*(1+a*x)^3//4*(1+-1*a*x)^1//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+231//1024*2^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+231//1280*a^-1*c^2*(1+a*x)^3//4*(1+-1*a*x)^5//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+231//2048*2^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((c+-1*c*a^2*x^2)^3//2*exp((1/2)*arctanh(a*x)), x) == :(-35//128*c*2^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-35//256*c*2^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-7//24*c*a^-1*(1+a*x)^3//4*(1+-1*a*x)^9//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//4*c*a^-1*(1+a*x)^7//4*(1+-1*a*x)^9//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+7//32*c*a^-1*(1+a*x)^3//4*(1+-1*a*x)^5//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+35//64*c*a^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+35//128*c*2^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+35//256*c*2^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp((1/2)*arctanh(a*x)), x) == :(-3//8*2^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-3//16*2^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*a^-1*(1+a*x)^3//4*(1+-1*a*x)^5//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+3//4*a^-1*(1+a*x)^3//4*(1+-1*a*x)^1//4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+3//8*2^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+3//16*2^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp((1/2)*arctanh(a*x)), x) == :(2^(1/2)*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctan(1+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+(1/2)*2^(1/2)*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+-1*2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1*2^(1/2)*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arctan(1+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4)+-1//2*2^(1/2)*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+(1+a*x)^-1//2*(1+-1*a*x)^(1/2)+2^(1/2)*(1+a*x)^-1//4*(1+-1*a*x)^1//4))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp((1/2)*arctanh(a*x)), x) == :(-2//3*a^-1*c^-1*(c+-1*c*a^2*x^2)^-1//2*(1+-2*a*x)*exp((1/2)*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp((1/2)*arctanh(a*x)), x) == :(-16//35*a^-1*c^-2*(c+-1*c*a^2*x^2)^-1//2*(1+-2*a*x)*exp((1/2)*arctanh(a*x))+-2//35*a^-1*c^-1*(c+-1*c*a^2*x^2)^-3//2*(1+-6*a*x)*exp((1/2)*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp((1/2)*arctanh(a*x)), x) == :(-256//693*a^-1*c^-3*(c+-1*c*a^2*x^2)^-1//2*(1+-2*a*x)*exp((1/2)*arctanh(a*x))+-32//693*a^-1*c^-2*(c+-1*c*a^2*x^2)^-3//2*(1+-6*a*x)*exp((1/2)*arctanh(a*x))+-2//99*a^-1*c^-1*(c+-1*c*a^2*x^2)^-5//2*(1+-10*a*x)*exp((1/2)*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-9//2*exp((1/2)*arctanh(a*x)), x) == :(-2048//6435*a^-1*c^-4*(c+-1*c*a^2*x^2)^-1//2*(1+-2*a*x)*exp((1/2)*arctanh(a*x))+-256//6435*a^-1*c^-3*(c+-1*c*a^2*x^2)^-3//2*(1+-6*a*x)*exp((1/2)*arctanh(a*x))+-112//6435*a^-1*c^-2*(c+-1*c*a^2*x^2)^-5//2*(1+-10*a*x)*exp((1/2)*arctanh(a*x))+-2//195*a^-1*c^-1*(c+-1*c*a^2*x^2)^-7//2*(1+-14*a*x)*exp((1/2)*arctanh(a*x)))
@test integrate(x^3*(c+-1*c*a^2*x^2)^-5//4*exp((1/2)*arctanh(a*x)), x) == :(a^-4*c^-1*(1+-1*a*x)^-1//2*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+2*a^-4*c^-1*(1+-1*a*x)^(1/2)*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+-2//3*a^-4*c^-1*(1+-1*a*x)^3//2*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+(1/2)*2^(1/2)*a^-4*c^-1*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4*arctanh((1/2)*2^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-5//4*exp((1/2)*arctanh(a*x)), x) == :(a^-3*c^-1*(1+-1*a*x)^-1//2*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+2*a^-3*c^-1*(1+-1*a*x)^(1/2)*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+-1//2*2^(1/2)*a^-3*c^-1*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4*arctanh((1/2)*2^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x*(c+-1*c*a^2*x^2)^-5//4*exp((1/2)*arctanh(a*x)), x) == :(a^-2*c^-1*(1+-1*a*x)^-1//2*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+(1/2)*2^(1/2)*a^-2*c^-1*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4*arctanh((1/2)*2^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^-5//4*exp((1/2)*arctanh(a*x)), x) == :(a^-1*c^-1*(1+-1*a*x)^-1//2*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+-1//2*2^(1/2)*a^-1*c^-1*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4*arctanh((1/2)*2^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-5//4*exp((1/2)*arctanh(a*x)), x) == :(c^-1*(1+-1*a*x)^-1//2*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+-2*c^-1*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4*arctanh((1+-1*a*x)^(1/2))+(1/2)*2^(1/2)*c^-1*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4*arctanh((1/2)*2^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-5//4*exp((1/2)*arctanh(a*x)), x) == :(-1*a*c^-1*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4*arctanh((1+-1*a*x)^(1/2))+-1*c^-1*x^-1*(1+-1*a*x)^-1//2*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+2*a*c^-1*(1+-1*a*x)^-1//2*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4+-1//2*a*2^(1/2)*c^-1*(1+-1*a^2*x^2)^1//4*(c+-1*c*a^2*x^2)^-1//4*arctanh((1/2)*2^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-9//8*exp((1/2)*arctanh(a*x)), x) == :(4//3*a^-3*c^-1*(c+-1*c*a^2*x^2)^-1//8*(2+-1*a*x)*exp((1/2)*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-1*exp(n*arctanh(a*x)), x) == :(a^-1*c^-1*n^-1*exp(n*arctanh(a*x)))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-2*exp(n*arctanh(a*x)), x) == :(-1*a^-3*c^-2*n^-1*(4+-1*n^2)^-1*(2+-1*n^2)*exp(n*arctanh(a*x))+-1*a^-3*c^-2*(1+-1*a^2*x^2)^-1*(4+-1*n^2)^-1*(n+-2*a*x)*exp(n*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(n*arctanh(a*x)), x) == :(2*a^-1*c^-2*n^-1*(4+-1*n^2)^-1*exp(n*arctanh(a*x))+-1*a^-1*c^-2*(1+-1*a^2*x^2)^-1*(4+-1*n^2)^-1*(n+-2*a*x)*exp(n*arctanh(a*x)))
@test integrate(x*(c+-1*c*a^2*x^2)^-3//2*exp(n*arctanh(a*x)), x) == :(a^-2*c^-1*(1+-1*n^2)^-1*(c+-1*c*a^2*x^2)^-1//2*(1+-1*a*n*x)*exp(n*arctanh(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(n*arctanh(a*x)), x) == :(-1*a^-1*c^-1*(1+-1*n^2)^-1*(c+-1*c*a^2*x^2)^-1//2*(n+-1*a*x)*exp(n*arctanh(a*x)))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-5//2*exp(n*arctanh(a*x)), x) == :(-1*a^-3*c^-1*(9+-1*n^2)^-1*(c+-1*c*a^2*x^2)^-3//2*(n+-3*a*x)*exp(n*arctanh(a*x))+a^-3*c^-2*(c+-1*c*a^2*x^2)^-1//2*(9+n^4+-10*n^2)^-1*(3+-1*n^2)*(n+-1*a*x)*exp(n*arctanh(a*x)))
@test integrate(x*(c+-1*c*a^2*x^2)^-5//2*exp(n*arctanh(a*x)), x) == :(1//3*a^-2*c^-1*(c+-1*c*a^2*x^2)^-3//2*exp(n*arctanh(a*x))+2*n*a^-2*c^-2*(c+-1*c*a^2*x^2)^-1//2*(9+n^4+-10*n^2)^-1*(n+-1*a*x)*exp(n*arctanh(a*x))+1//3*n*a^-2*c^-1*(9+-1*n^2)^-1*(c+-1*c*a^2*x^2)^-3//2*(n+-3*a*x)*exp(n*arctanh(a*x)))
@test integrate((1+-1*a^2*x^2)^(-1p)*exp((2+2p)*arctanh(a*x)), x) == :(a^-1*p^-1*(1+-1*a*x)^(-2p)+a^-1*(1+-2p)^-1*(1+-1*a*x)^(1+-2p))
@test integrate((c+-1*c*a^2*x^2)^(-1p)*exp((2+2p)*arctanh(a*x)), x) == :(a^-1*p^-1*(1+-1*a*x)^(-2p)*(1+-1*a^2*x^2)^p*(c+-1*c*a^2*x^2)^(-1p)+a^-1*(1+-2p)^-1*(1+-1*a*x)^(1+-2p)*(1+-1*a^2*x^2)^p*(c+-1*c*a^2*x^2)^(-1p))
@test integrate((c+-1*c*a^2*x^2)^p*exp(2*p*arctanh(a*x)), x) == :(a^-1*(1+2p)^-1*(1+a*x)^(1+2p)*(1+-1*a^2*x^2)^(-1p)*(c+-1*c*a^2*x^2)^p)
@test integrate((c+-1*c*a^2*x^2)^p*exp(-2*p*arctanh(a*x)), x) == :(-1*a^-1*(1+2p)^-1*(1+-1*a*x)^(1+2p)*(1+-1*a^2*x^2)^(-1p)*(c+-1*c*a^2*x^2)^p)
@test integrate(x^2*(c+-1*c*a^2*x^2)^(-1+-1//2*n^2)*exp(n*arctanh(a*x)), x) == :(a^-3*c^-1*n^-1*(1+-1*n^2)^-1*(c+-1*c*a^2*x^2)^(-1//2*n^2)*(1+-1*a*n*x)*exp(n*arctanh(a*x)))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-19*exp(6*arctanh(a*x)), x) == :(-1//210*a^-3*c^-19*(1+a*x)^-15*(1+-1*a*x)^-21*(1+-6*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-9*exp(4*arctanh(a*x)), x) == :(-1//60*a^-3*c^-9*(1+a*x)^-6*(1+-1*a*x)^-10*(1+-4*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-3*exp(2*arctanh(a*x)), x) == :(-1//6*a^-3*c^-3*(1+a*x)^-1*(1+-1*a*x)^-3*(1+-2*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-3*exp(-2*arctanh(a*x)), x) == :(1//6*a^-3*c^-3*(1+a*x)^-3*(1+-1*a*x)^-1*(1+2*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-9*exp(-4*arctanh(a*x)), x) == :(1//60*a^-3*c^-9*(1+a*x)^-10*(1+-1*a*x)^-6*(1+4*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-27//2*exp(5*arctanh(a*x)), x) == :(-1//120*a^-3*c^-13*(1+a*x)^-10*(1+-1*a*x)^-15*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*(1+-5*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-11//2*exp(3*arctanh(a*x)), x) == :(-1//24*a^-3*c^-5*(1+a*x)^-3*(1+-1*a*x)^-6*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*(1+-3*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-3//2*exp(arctanh(a*x)), x) == :((1/2)*a^-3*c^-1*(1+-1*a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+1//4*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+3//4*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-3//2*exp(-1*arctanh(a*x)), x) == :(-3//4*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+-1//2*a^-3*c^-1*(1+a*x)^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2+-1//4*a^-3*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-11//2*exp(-3*arctanh(a*x)), x) == :(1//24*a^-3*c^-5*(1+a*x)^-6*(1+-1*a*x)^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*(1+3*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-27//2*exp(-5*arctanh(a*x)), x) == :(1//120*a^-3*c^-13*(1+a*x)^-15*(1+-1*a*x)^-10*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*(1+5*a*x))

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.6 Exponentials of inverse hyperbolic tangent functions.jl