\[ \int \left (7+5 x^2\right )^2 \left (2+x^2-x^4\right )^{3/2} \, dx \]
Optimal antiderivative \[ \frac {x \left (920 x^{2}+363\right ) \left (-x^{4}+x^{2}+2\right )^{\frac {3}{2}}}{99}-\frac {25 x \left (-x^{4}+x^{2}+2\right )^{\frac {5}{2}}}{11}+\frac {85942 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{495}-\frac {3392 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{165}+\frac {x \left (14889 x^{2}+11497\right ) \sqrt {-x^{4}+x^{2}+2}}{495} \]
command
integrate((5*x^2+7)^2*(-x^4+x^2+2)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {{\left (1125 \, x^{10} + 2350 \, x^{8} - 6160 \, x^{6} - 21404 \, x^{4} - 10627 \, x^{2} + 85942\right )} \sqrt {-x^{4} + x^{2} + 2}}{495 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-{\left (25 \, x^{8} + 45 \, x^{6} - 71 \, x^{4} - 189 \, x^{2} - 98\right )} \sqrt {-x^{4} + x^{2} + 2}, x\right ) \]