\[ \int \left (7+5 x^2\right )^3 \left (2+x^2-x^4\right )^{3/2} \, dx \]
Optimal antiderivative \[ \frac {x \left (374045 x^{2}+33792\right ) \left (-x^{4}+x^{2}+2\right )^{\frac {3}{2}}}{3003}-\frac {7825 x \left (-x^{4}+x^{2}+2\right )^{\frac {5}{2}}}{143}-\frac {125 x^{3} \left (-x^{4}+x^{2}+2\right )^{\frac {5}{2}}}{13}+\frac {31072528 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{15015}-\frac {3199778 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{5005}+\frac {x \left (5712051 x^{2}+2512273\right ) \sqrt {-x^{4}+x^{2}+2}}{15015} \]
command
Integrate[(7 + 5*x^2)^3*(2 + x^2 - x^4)^(3/2),x]
Mathematica 13.1 output
\[ \frac {-872614 x+11078615 x^3+13371048 x^5-1756521 x^7-4448240 x^9-1027775 x^{11}+388500 x^{13}+144375 x^{15}+31072528 i \sqrt {4+2 x^2-2 x^4} E\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )-41809125 i \sqrt {4+2 x^2-2 x^4} F\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )}{15015 \sqrt {2+x^2-x^4}} \]
Mathematica 12.3 output
\[ \text {\$Aborted} \]________________________________________________________________________________________