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