\[ \int \frac {\sqrt {2+e x}}{\sqrt {12-3 e^2 x^2}} \, dx \]
Optimal antiderivative \[ -\frac {2 \sqrt {3}\, \sqrt {-e x +2}}{3 e} \]
command
integrate((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
\[ -\frac {2}{3} \, \sqrt {3} {\left (\sqrt {-x e + 2} - 2\right )} e^{\left (-1\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {\sqrt {e x + 2}}{\sqrt {-3 \, e^{2} x^{2} + 12}}\,{d x} \]________________________________________________________________________________________