\[ \int x \coth ^{-1}(\tanh (a+b x))^2 \, dx \]
Optimal antiderivative \[ \frac {x \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{3}}{3 b}-\frac {\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{4}}{12 b^{2}} \]
command
integrate(x*arccoth(tanh(b*x+a))^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{4} \, b^{2} x^{4} - \frac {1}{3} \, {\left (-i \, \pi b - 2 \, a b\right )} x^{3} - \frac {1}{8} \, {\left (\pi ^{2} - 4 i \, \pi a - 4 \, a^{2}\right )} x^{2} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int x \operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{2}\,{d x} \]________________________________________________________________________________________