\[ \int \frac {1}{\sqrt {3+5 x^2+2 x^4}} \, dx \]
Optimal antiderivative \[ \frac {\left (x^{2}+1\right )^{\frac {3}{2}} \sqrt {\frac {1}{x^{2}+1}}\, \EllipticF \left (\frac {x}{\sqrt {x^{2}+1}}, \frac {\sqrt {3}}{3}\right ) \sqrt {\frac {2 x^{2}+3}{x^{2}+1}}\, \sqrt {3}}{3 \sqrt {2 x^{4}+5 x^{2}+3}} \]
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
\[ -\frac {1}{2} \, \sqrt {-2} {\rm ellipticF}\left (\frac {1}{3} \, \sqrt {3} \sqrt {-2} x, \frac {3}{2}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {1}{\sqrt {2 \, x^{4} + 5 \, x^{2} + 3}}, x\right ) \]