\[ \int \frac {(2+e x)^{9/2}}{\left (12-3 e^2 x^2\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {8 \left (-e x +2\right )^{\frac {3}{2}} \sqrt {3}}{9 e}+\frac {2 \left (-e x +2\right )^{\frac {5}{2}} \sqrt {3}}{45 e}+\frac {128 \sqrt {3}}{9 e \sqrt {-e x +2}}+\frac {32 \sqrt {3}\, \sqrt {-e x +2}}{3 e} \]
command
integrate((e*x+2)^(9/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2}{45} \, \sqrt {3} {\left ({\left (x e - 2\right )}^{2} \sqrt {-x e + 2} e^{4} - 20 \, {\left (-x e + 2\right )}^{\frac {3}{2}} e^{4} + 240 \, \sqrt {-x e + 2} e^{4}\right )} e^{\left (-5\right )} - \frac {1024}{45} \, \sqrt {3} e^{\left (-1\right )} + \frac {128 \, \sqrt {3} e^{\left (-1\right )}}{9 \, \sqrt {-x e + 2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________