\[ \int \frac {1}{\sqrt {2-5 x^2-3 x^4}} \, dx \]
Optimal antiderivative \[ \frac {\EllipticF \left (x \sqrt {3}, \frac {i \sqrt {6}}{6}\right ) \sqrt {6}}{6} \]
command
integrate(1/(-3*x^4-5*x^2+2)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {1}{6} \, \sqrt {3} \sqrt {2} {\rm ellipticF}\left (\sqrt {3} x, -\frac {1}{6}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {-3 \, x^{4} - 5 \, x^{2} + 2}}{3 \, x^{4} + 5 \, x^{2} - 2}, x\right ) \]