\[ \int \frac {\left (7+5 x^2\right )^4}{\left (2+x^2-x^4\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {165239 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{18}+\frac {31921 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{6}+\frac {x \left (83489 x^{2}+83585\right )}{18 \sqrt {-x^{4}+x^{2}+2}}+\frac {625 x \sqrt {-x^{4}+x^{2}+2}}{3} \]
command
integrate((5*x^2+7)^4/(-x^4+x^2+2)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (1875 \, x^{6} + 39000 \, x^{4} - 128162 \, x^{2} - 165239\right )} \sqrt {-x^{4} + x^{2} + 2}}{9 \, {\left (x^{5} - x^{3} - 2 \, x\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {{\left (625 \, x^{8} + 3500 \, x^{6} + 7350 \, x^{4} + 6860 \, x^{2} + 2401\right )} \sqrt {-x^{4} + x^{2} + 2}}{x^{8} - 2 \, x^{6} - 3 \, x^{4} + 4 \, x^{2} + 4}, x\right ) \]