\[ \int \frac {1}{\sqrt {2+3 x^2+x^4}} \, dx \]
Optimal antiderivative \[ \frac {\left (x^{2}+1\right )^{\frac {3}{2}} \sqrt {\frac {1}{x^{2}+1}}\, \EllipticF \left (\frac {x}{\sqrt {x^{2}+1}}, \frac {\sqrt {2}}{2}\right ) \sqrt {2}\, \sqrt {\frac {x^{2}+2}{x^{2}+1}}}{2 \sqrt {x^{4}+3 x^{2}+2}} \]
command
integrate(1/(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
\[ -i \, {\rm ellipticF}\left (\frac {1}{2} i \, \sqrt {2} x, 2\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {1}{\sqrt {x^{4} + 3 \, x^{2} + 2}}, x\right ) \]