\[ \int \frac {1}{\sqrt {3+7 x^2-2 x^4}} \, dx \]
Optimal antiderivative \[ \frac {\EllipticF \left (\frac {2 x}{\sqrt {7+\sqrt {73}}}, \frac {7 i \sqrt {6}}{12}+\frac {i \sqrt {438}}{12}\right ) \sqrt {2}}{\sqrt {-7+\sqrt {73}}} \]
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
\[ \frac {1}{72} \, {\left (\sqrt {73} \sqrt {6} \sqrt {3} + 7 \, \sqrt {6} \sqrt {3}\right )} \sqrt {\sqrt {73} - 7} {\rm ellipticF}\left (\frac {1}{6} \, \sqrt {6} x \sqrt {\sqrt {73} - 7}, -\frac {7}{12} \, \sqrt {73} - \frac {61}{12}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {-2 \, x^{4} + 7 \, x^{2} + 3}}{2 \, x^{4} - 7 \, x^{2} - 3}, x\right ) \]