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