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