\[ \int \frac {\coth ^{-1}(\tanh (a+b x))^3}{x^6} \, dx \]
Optimal antiderivative \[ \frac {b \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{4}}{20 x^{4} \left (b x -\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )\right )^{2}}+\frac {\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{4}}{5 x^{5} \left (b x -\mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )\right )} \]
command
integrate(arccoth(tanh(b*x+a))^3/x^6,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {40 \, b^{3} x^{3} + 40 i \, \pi b^{2} x^{2} + 80 \, a b^{2} x^{2} - 15 \, \pi ^{2} b x + 60 i \, \pi a b x + 60 \, a^{2} b x - 2 i \, \pi ^{3} - 12 \, \pi ^{2} a + 24 i \, \pi a^{2} + 16 \, a^{3}}{80 \, x^{5}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {\operatorname {arcoth}\left (\tanh \left (b x + a\right )\right )^{3}}{x^{6}}\,{d x} \]________________________________________________________________________________________