\[ \int \frac {1}{\sqrt {2+e x} \sqrt {12-3 e^2 x^2}} \, dx \]
Optimal antiderivative \[ -\frac {\arctanh \left (\frac {\sqrt {-e x +2}}{2}\right ) \sqrt {3}}{3 e} \]
command
integrate(1/(e*x+2)^(1/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {1}{6} \, \sqrt {3} {\left (\log \left (\sqrt {-x e + 2} + 2\right ) - \log \left (-\sqrt {-x e + 2} + 2\right )\right )} e^{\left (-1\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {1}{\sqrt {-3 \, e^{2} x^{2} + 12} \sqrt {e x + 2}}\,{d x} \]________________________________________________________________________________________