\[ \int x \coth ^{-1}(\tanh (a+b x))^3 \, dx \]
Optimal antiderivative \[ \frac {x \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{4}}{4 b}-\frac {\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{5}}{20 b^{2}} \]
command
integrate(x*arccoth(tanh(b*x+a))^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{5} \, b^{3} x^{5} - \frac {3}{8} \, {\left (-i \, \pi b^{2} - 2 \, a b^{2}\right )} x^{4} - \frac {1}{4} \, {\left (\pi ^{2} b - 4 i \, \pi a b - 4 \, a^{2} b\right )} x^{3} - \frac {1}{16} \, {\left (i \, \pi ^{3} + 6 \, \pi ^{2} a - 12 i \, \pi a^{2} - 8 \, a^{3}\right )} x^{2} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int x \operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{3}\,{d x} \]________________________________________________________________________________________