\[ \int \left (7+5 x^2\right )^2 \sqrt {2+x^2-x^4} \, dx \]
Optimal antiderivative \[ -\frac {25 x \left (-x^{4}+x^{2}+2\right )^{\frac {3}{2}}}{7}+\frac {2045 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{21}-\frac {79 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{7}+\frac {x \left (354 x^{2}+275\right ) \sqrt {-x^{4}+x^{2}+2}}{21} \]
command
integrate((5*x^2+7)^2*(-x^4+x^2+2)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {{\left (75 \, x^{6} + 279 \, x^{4} + 125 \, x^{2} - 2045\right )} \sqrt {-x^{4} + x^{2} + 2}}{21 \, x} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left ({\left (25 \, x^{4} + 70 \, x^{2} + 49\right )} \sqrt {-x^{4} + x^{2} + 2}, x\right ) \]