\[ \int \frac {\left (7+5 x^2\right )^5}{\left (2+x^2-x^4\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {3482293 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{18}+\frac {627857 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{6}+\frac {x \left (1419793 x^{2}+1419985\right )}{18 \sqrt {-x^{4}+x^{2}+2}}+\frac {27500 x \sqrt {-x^{4}+x^{2}+2}}{3}+625 x^{3} \sqrt {-x^{4}+x^{2}+2} \]
command
Integrate[(7 + 5*x^2)^5/(2 + x^2 - x^4)^(3/2),x]
Mathematica 13.1 output
\[ \frac {1749985 x+1607293 x^3-153750 x^5-11250 x^7-3482293 i \sqrt {4+2 x^2-2 x^4} E\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )+4281654 i \sqrt {4+2 x^2-2 x^4} F\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )}{18 \sqrt {2+x^2-x^4}} \]
Mathematica 12.3 output
\[ \text {\$Aborted} \]________________________________________________________________________________________