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