\[ \int \frac {1}{\left (c (a+b x)^3\right )^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {2}{13 b \,c^{2} \left (b x +a \right )^{5} \sqrt {c \left (b x +a \right )^{3}}} \]
command
integrate(1/(c*(b*x+a)^3)^(5/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {2 \, c^{4}}{13 \, {\left (b c x + a c\right )}^{\frac {13}{2}} b \mathrm {sgn}\left (b x + a\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {sage}_{0} x \]________________________________________________________________________________________