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