\[ \int \frac {1}{\sqrt {3-3 x^2-2 x^4}} \, dx \]
Optimal antiderivative \[ \frac {\EllipticF \left (\frac {2 x}{\sqrt {-3+\sqrt {33}}}, \frac {i \sqrt {22}}{4}-\frac {i \sqrt {6}}{4}\right ) \sqrt {2}}{\sqrt {3+\sqrt {33}}} \]
command
integrate(1/(-2*x^4-3*x^2+3)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {1}{24} \, {\left (\sqrt {11} \sqrt {6} - \sqrt {6} \sqrt {3}\right )} \sqrt {\sqrt {11} \sqrt {3} + 3} {\rm ellipticF}\left (\frac {1}{6} \, \sqrt {6} \sqrt {\sqrt {11} \sqrt {3} + 3} x, \frac {1}{4} \, \sqrt {11} \sqrt {3} - \frac {7}{4}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {-2 \, x^{4} - 3 \, x^{2} + 3}}{2 \, x^{4} + 3 \, x^{2} - 3}, x\right ) \]