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