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