\[ \int \frac {1}{\sqrt {3+7 x^2+2 x^4}} \, dx \]
Optimal antiderivative \[ \frac {\left (2 x^{2}+1\right )^{\frac {3}{2}} \sqrt {\frac {1}{2 x^{2}+1}}\, \EllipticF \left (\frac {x \sqrt {2}}{\sqrt {2 x^{2}+1}}, \frac {\sqrt {30}}{6}\right ) \sqrt {\frac {x^{2}+3}{2 x^{2}+1}}\, \sqrt {6}}{6 \sqrt {2 x^{4}+7 x^{2}+3}} \]
command
integrate(1/(2*x^4+7*x^2+3)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -i \, {\rm ellipticF}\left (\frac {1}{3} i \, \sqrt {3} x, 6\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {1}{\sqrt {2 \, x^{4} + 7 \, x^{2} + 3}}, x\right ) \]