\[ \int \frac {\coth ^{-1}(\tanh (a+b x))^3}{x^3} \, dx \]
Optimal antiderivative \[ 3 b^{3} x -\frac {3 b \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{2}}{2 x}-\frac {\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{3}}{2 x^{2}}-3 b^{2} \left (b x -\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )\right ) \ln \left (x \right ) \]
command
integrate(arccoth(tanh(b*x+a))^3/x^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ b^{3} x + \frac {3}{2} \, {\left (i \, \pi b^{2} + 2 \, a b^{2}\right )} \log \left (x\right ) + \frac {12 \, \pi ^{2} b x - 48 i \, \pi a b x - 48 \, a^{2} b x + i \, \pi ^{3} + 6 \, \pi ^{2} a - 12 i \, \pi a^{2} - 8 \, a^{3}}{16 \, x^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {\operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{3}}{x^{3}}\,{d x} \]________________________________________________________________________________________