\[ \int e^{2 \text {csch}^{-1}(a x)} x^3 \, dx \]
Optimal antiderivative \[ \frac {x^{2}}{a^{2}}+\frac {2 \left (1+\frac {1}{a^{2} x^{2}}\right )^{\frac {3}{2}} x^{3}}{3 a}+\frac {x^{4}}{4} \]
command
integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {a^{2} x^{2} + 1}{2 \, a^{4}} - \frac {2 \, {\left | a \right |} \mathrm {sgn}\left (x\right )}{3 \, a^{5}} + \frac {8 \, {\left (a^{2} x^{2} + 1\right )}^{\frac {3}{2}} a^{2} {\left | a \right |} \mathrm {sgn}\left (x\right ) + 3 \, {\left (a^{2} x^{2} + 1\right )}^{2} a^{3}}{12 \, a^{7}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________