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