\[ \int \frac {\left (12-3 e^2 x^2\right )^{3/2}}{(2+e x)^{9/2}} \, dx \]
Optimal antiderivative \[ -\frac {3 \left (-e x +2\right )^{\frac {3}{2}} \sqrt {3}}{2 e \left (e x +2\right )^{2}}-\frac {9 \arctanh \left (\frac {\sqrt {-e x +2}}{2}\right ) \sqrt {3}}{8 e}+\frac {9 \sqrt {3}\, \sqrt {-e x +2}}{4 e \left (e x +2\right )} \]
command
integrate((-3*e^2*x^2+12)^(3/2)/(e*x+2)^(9/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {3}{16} \, \sqrt {3} {\left (\frac {4 \, {\left (5 \, {\left (-x e + 2\right )}^{\frac {3}{2}} - 12 \, \sqrt {-x e + 2}\right )}}{{\left (x e + 2\right )}^{2}} + 3 \, \log \left (\sqrt {-x e + 2} + 2\right ) - 3 \, \log \left (-\sqrt {-x e + 2} + 2\right )\right )} e^{\left (-1\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: RuntimeError} \]________________________________________________________________________________________