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