\[ \int x^3 \coth ^{-1}(\tanh (a+b x))^3 \, dx \]
Optimal antiderivative \[ -\frac {b^{3} x^{7}}{140}+\frac {b^{2} x^{6} \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )}{20}-\frac {3 b \,x^{5} \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{2}}{20}+\frac {x^{4} \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{3}}{4} \]
command
integrate(x^3*arccoth(tanh(b*x+a))^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{7} \, b^{3} x^{7} - \frac {1}{4} \, {\left (-i \, \pi b^{2} - 2 \, a b^{2}\right )} x^{6} - \frac {3}{20} \, {\left (\pi ^{2} b - 4 i \, \pi a b - 4 \, a^{2} b\right )} x^{5} - \frac {1}{32} \, {\left (i \, \pi ^{3} + 6 \, \pi ^{2} a - 12 i \, \pi a^{2} - 8 \, a^{3}\right )} x^{4} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int x^{3} \operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{3}\,{d x} \]________________________________________________________________________________________