\[ \int \frac {1}{(2+e x)^{5/2} \sqrt {12-3 e^2 x^2}} \, dx \]
Optimal antiderivative \[ -\frac {\arctanh \left (\frac {\sqrt {-e x +2}}{2}\right ) \sqrt {3}}{128 e}-\frac {\sqrt {3}\, \sqrt {-e x +2}}{24 e \left (e x +2\right )^{2}}-\frac {\sqrt {3}\, \sqrt {-e x +2}}{64 e \left (e x +2\right )} \]
command
integrate(1/(e*x+2)^(5/2)/(-3*e^2*x^2+12)^(1/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{768} \, \sqrt {3} {\left (\frac {4 \, {\left (3 \, {\left (-x e + 2\right )}^{\frac {3}{2}} - 20 \, \sqrt {-x e + 2}\right )}}{{\left (x e + 2\right )}^{2}} - 3 \, \log \left (\sqrt {-x e + 2} + 2\right ) + 3 \, \log \left (-\sqrt {-x e + 2} + 2\right )\right )} e^{\left (-1\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {sage}_{0} x \]________________________________________________________________________________________