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