\[ \int \left (7+5 x^2\right )^4 \left (2+x^2-x^4\right )^{3/2} \, dx \]
Optimal antiderivative \[ -\frac {x \left (-1581440 x^{2}+69817\right ) \left (-x^{4}+x^{2}+2\right )^{\frac {3}{2}}}{1001}-\frac {132300 x \left (-x^{4}+x^{2}+2\right )^{\frac {5}{2}}}{143}-\frac {11750 x^{3} \left (-x^{4}+x^{2}+2\right )^{\frac {5}{2}}}{39}-\frac {125 x^{5} \left (-x^{4}+x^{2}+2\right )^{\frac {5}{2}}}{3}+\frac {124141422 \EllipticE \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{5005}-\frac {50794416 \EllipticF \left (\frac {x \sqrt {2}}{2}, i \sqrt {2}\right )}{5005}+\frac {3 x \left (7837383 x^{2}+2193559\right ) \sqrt {-x^{4}+x^{2}+2}}{5005} \]
command
Integrate[(7 + 5*x^2)^4*(2 + x^2 - x^4)^(3/2),x]
Mathematica 13.1 output
\[ \frac {-75836958 x+48624305 x^3+172881581 x^5+32834763 x^7-36649955 x^9-24642275 x^{11}-1556625 x^{13}+2646875 x^{15}+625625 x^{17}+372424266 i \sqrt {4+2 x^2-2 x^4} E\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )-482444775 i \sqrt {4+2 x^2-2 x^4} F\left (i \sinh ^{-1}(x)|-\frac {1}{2}\right )}{15015 \sqrt {2+x^2-x^4}} \]
Mathematica 12.3 output
\[ \text {\$Aborted} \]________________________________________________________________________________________