\[ \int \frac {1}{\sqrt {2+5 x^2-9 x^4}} \, dx \]
Optimal antiderivative \[ \frac {\EllipticF \left (\frac {3 x \sqrt {2}}{\sqrt {5+\sqrt {97}}}, \frac {5 i \sqrt {2}}{12}+\frac {i \sqrt {194}}{12}\right ) \sqrt {2}}{\sqrt {-5+\sqrt {97}}} \]
command
integrate(1/(-9*x^4+5*x^2+2)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {1}{72} \, {\left (\sqrt {97} \sqrt {2} + 5 \, \sqrt {2}\right )} \sqrt {\sqrt {97} - 5} {\rm ellipticF}\left (\frac {1}{2} \, x \sqrt {\sqrt {97} - 5}, -\frac {5}{36} \, \sqrt {97} - \frac {61}{36}\right ) \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {\sqrt {-9 \, x^{4} + 5 \, x^{2} + 2}}{9 \, x^{4} - 5 \, x^{2} - 2}, x\right ) \]