\[ \int \frac {\sqrt {12-3 e^2 x^2}}{\sqrt {2+e x}} \, dx \]
Optimal antiderivative \[ -\frac {2 \left (-e x +2\right )^{\frac {3}{2}} \sqrt {3}}{3 e} \]
command
integrate((-3*e^2*x^2+12)^(1/2)/(e*x+2)^(1/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {2}{3} \, \sqrt {3} {\left ({\left (-x e + 2\right )}^{\frac {3}{2}} - 8\right )} e^{\left (-1\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {\sqrt {-3 \, e^{2} x^{2} + 12}}{\sqrt {e x + 2}}\,{d x} \]________________________________________________________________________________________