\[ \int \frac {\left (7+5 x^2\right )^2}{\sqrt {2+x^2-x^4}} \, dx \]
Optimal antiderivative \[ \frac {260 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{3}-21 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )-\frac {25 x \sqrt {-x^{4}+x^{2}+2}}{3} \]
command
integrate((5*x^2+7)^2/(-x^4+x^2+2)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {5 \, \sqrt {-x^{4} + x^{2} + 2} {\left (5 \, x^{2} + 52\right )}}{3 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-\frac {{\left (25 \, x^{4} + 70 \, x^{2} + 49\right )} \sqrt {-x^{4} + x^{2} + 2}}{x^{4} - x^{2} - 2}, x\right ) \]