14.94 Problem number 922

\[ \int \frac {(2+e x)^{3/2}}{\left (12-3 e^2 x^2\right )^{3/2}} \, dx \]

Optimal antiderivative \[ \frac {2 \sqrt {3}}{9 e \sqrt {-e x +2}} \]

command

integrate((e*x+2)^(3/2)/(-3*e^2*x^2+12)^(3/2),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ -\frac {1}{9} \, \sqrt {3} e^{\left (-1\right )} + \frac {2 \, \sqrt {3} e^{\left (-1\right )}}{9 \, \sqrt {-x e + 2}} \]

Giac 1.7.0 via sagemath 9.3 output

\[ \mathit {sage}_{0} x \]________________________________________________________________________________________