\[ \int \left (7+5 x^2\right ) \left (2+x^2-x^4\right )^{3/2} \, dx \]
Optimal antiderivative \[ \frac {x \left (35 x^{2}+48\right ) \left (-x^{4}+x^{2}+2\right )^{\frac {3}{2}}}{63}+\frac {4432 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{315}+\frac {418 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{105}+\frac {x \left (669 x^{2}+1087\right ) \sqrt {-x^{4}+x^{2}+2}}{315} \]
command
integrate((5*x^2+7)*(-x^4+x^2+2)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\frac {{\left (175 \, x^{8} + 65 \, x^{6} - 1259 \, x^{4} - 1567 \, x^{2} + 4432\right )} \sqrt {-x^{4} + x^{2} + 2}}{315 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (-{\left (5 \, x^{6} + 2 \, x^{4} - 17 \, x^{2} - 14\right )} \sqrt {-x^{4} + x^{2} + 2}, x\right ) \]