\[ \int \frac {\left (7+5 x^2\right )^4}{\left (2+x^2-x^4\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {165239 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{18}+\frac {31921 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{6}+\frac {x \left (83489 x^{2}+83585\right )}{18 \sqrt {-x^{4}+x^{2}+2}}+\frac {625 x \sqrt {-x^{4}+x^{2}+2}}{3} \]
command
Integrate[(7 + 5*x^2)^4/(2 + x^2 - x^4)^(3/2),x]
Mathematica 13.1 output
\[ \frac {91085 x+87239 x^3-3750 x^5-165239 i \sqrt {4+2 x^2-2 x^4} E\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )+199977 i \sqrt {4+2 x^2-2 x^4} F\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )}{18 \sqrt {2+x^2-x^4}} \]
Mathematica 12.3 output
\[ \text {\$Aborted} \]________________________________________________________________________________________