\[ \int \frac {1}{\left (\frac {b}{x^3}\right )^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {2 x^{4}}{11 b \sqrt {\frac {b}{x^{3}}}} \]
command
integrate(1/(b/x^3)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 \, \sqrt {b x} x^{5}}{11 \, b^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {1}{\left (\frac {b}{x^{3}}\right )^{\frac {3}{2}}}\,{d x} \]________________________________________________________________________________________