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