\[ \int \frac {1}{\left (4+12 x+9 x^2\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {1}{6 \left (2+3 x \right ) \sqrt {\left (2+3 x \right )^{2}}} \]
command
integrate(1/(9*x^2+12*x+4)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {1}{6 \, {\left (3 \, x + 2\right )}^{2} \mathrm {sgn}\left (3 \, x + 2\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {sage}_{0} x \]________________________________________________________________________________________