\[ \int \frac {\left (12-3 e^2 x^2\right )^{3/2}}{(2+e x)^{5/2}} \, dx \]
Optimal antiderivative \[ \frac {2 \left (-e x +2\right )^{\frac {3}{2}} \sqrt {3}}{e}-\frac {48 \arctanh \left (\frac {\sqrt {-e x +2}}{2}\right ) \sqrt {3}}{e}+\frac {24 \sqrt {3}\, \sqrt {-e x +2}}{e} \]
command
integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(5/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 2 \, \sqrt {3} {\left ({\left (-x e + 2\right )}^{\frac {3}{2}} + 12 \, \sqrt {-x e + 2} - 12 \, \log \left (\sqrt {-x e + 2} + 2\right ) + 12 \, \log \left (-\sqrt {-x e + 2} + 2\right )\right )} e^{\left (-1\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: RuntimeError} \]________________________________________________________________________________________