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