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