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