\[ \int \frac {x}{\coth ^{-1}(\tanh (a+b x))^3} \, dx \]
Optimal antiderivative \[ -\frac {x}{2 b \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{2}}-\frac {1}{2 b^{2} \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )} \]
command
integrate(x/arccoth(tanh(b*x+a))^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {i \, \pi + 4 \, b x + 2 \, a}{4 \, b^{4} x^{2} + 4 i \, \pi b^{3} x + 8 \, a b^{3} x - \pi ^{2} b^{2} + 4 i \, \pi a b^{2} + 4 \, a^{2} b^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {x}{\operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{3}}\,{d x} \]________________________________________________________________________________________