\[ \int \frac {(2+e x)^{5/2}}{\left (12-3 e^2 x^2\right )^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {8 \sqrt {3}}{9 e \sqrt {-e x +2}}+\frac {2 \sqrt {3}\, \sqrt {-e x +2}}{9 e} \]
command
integrate((e*x+2)^(5/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2}{9} \, \sqrt {3} \sqrt {-x e + 2} e^{\left (-1\right )} - \frac {8}{9} \, \sqrt {3} e^{\left (-1\right )} + \frac {8 \, \sqrt {3} e^{\left (-1\right )}}{9 \, \sqrt {-x e + 2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________