\[ \int \frac {x}{\left (9+12 x+4 x^2\right )^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {1}{12 \left (4 x^{2}+12 x +9\right )^{\frac {3}{2}}}+\frac {3}{16 \left (3+2 x \right ) \left (4 x^{2}+12 x +9\right )^{\frac {3}{2}}} \]
command
integrate(x/(4*x^2+12*x+9)^(5/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {8 \, x + 3}{48 \, {\left (2 \, x + 3\right )}^{4} \mathrm {sgn}\left (2 \, x + 3\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {sage}_{0} x \]________________________________________________________________________________________