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