\[ \int \left (7+5 x^2\right )^3 \sqrt {2+x^2-x^4} \, dx \]
Optimal antiderivative \[ -\frac {1825 x \left (-x^{4}+x^{2}+2\right )^{\frac {3}{2}}}{21}-\frac {125 x^{3} \left (-x^{4}+x^{2}+2\right )^{\frac {3}{2}}}{9}+\frac {79411 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{63}-\frac {8735 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{21}+\frac {x \left (14691 x^{2}+5956\right ) \sqrt {-x^{4}+x^{2}+2}}{63} \]
command
integrate((5*x^2+7)^3*(-x^4+x^2+2)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (875 \, x^{8} + 4600 \, x^{6} + 7466 \, x^{4} - 4994 \, x^{2} - 79411\right )} \sqrt {-x^{4} + x^{2} + 2}}{63 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left ({\left (125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343\right )} \sqrt {-x^{4} + x^{2} + 2}, x\right ) \]