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