\[ \int \left (7+5 x^2\right )^2 \left (2+x^2-x^4\right )^{3/2} \, dx \]
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[(7 + 5*x^2)^2*(2 + x^2 - x^4)^(3/2),x]
Mathematica 13.1 output
\[ \frac {21254 x+53435 x^3+23097 x^5-19944 x^7-10760 x^9+1225 x^{11}+1125 x^{13}+85942 i \sqrt {4+2 x^2-2 x^4} E\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )-123825 i \sqrt {4+2 x^2-2 x^4} F\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )}{495 \sqrt {2+x^2-x^4}} \]
Mathematica 12.3 output
\[ \text {\$Aborted} \]________________________________________________________________________________________