\[ \int \frac {\left (7+5 x^2\right )^3}{\left (2+x^2-x^4\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {7147 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{18}+\frac {1763 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{6}+\frac {x \left (4897 x^{2}+4945\right )}{18 \sqrt {-x^{4}+x^{2}+2}} \]
command
integrate((5*x^2+7)^3/(-x^4+x^2+2)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (1125 \, x^{4} - 6046 \, x^{2} - 7147\right )} \sqrt {-x^{4} + x^{2} + 2}}{9 \, {\left (x^{5} - x^{3} - 2 \, x\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343\right )} \sqrt {-x^{4} + x^{2} + 2}}{x^{8} - 2 \, x^{6} - 3 \, x^{4} + 4 \, x^{2} + 4}, x\right ) \]