\[ \int \left (7+5 x^2\right )^2 \left (2+3 x^2+x^4\right )^{3/2} \, dx \]
Optimal antiderivative \[ \frac {x \left (2240 x^{2}+7281\right ) \left (x^{4}+3 x^{2}+2\right )^{\frac {3}{2}}}{693}+\frac {25 x \left (x^{4}+3 x^{2}+2\right )^{\frac {5}{2}}}{11}+\frac {742 x \left (x^{2}+2\right )}{15 \sqrt {x^{4}+3 x^{2}+2}}-\frac {742 \left (x^{2}+1\right )^{\frac {3}{2}} \sqrt {\frac {1}{x^{2}+1}}\, \EllipticE \left (\frac {x}{\sqrt {x^{2}+1}}, \frac {\sqrt {2}}{2}\right ) \sqrt {2}\, \sqrt {\frac {x^{2}+2}{x^{2}+1}}}{15 \sqrt {x^{4}+3 x^{2}+2}}+\frac {13879 \left (x^{2}+1\right )^{\frac {3}{2}} \sqrt {\frac {1}{x^{2}+1}}\, \EllipticF \left (\frac {x}{\sqrt {x^{2}+1}}, \frac {\sqrt {2}}{2}\right ) \sqrt {2}\, \sqrt {\frac {x^{2}+2}{x^{2}+1}}}{385 \sqrt {x^{4}+3 x^{2}+2}}+\frac {x \left (10643 x^{2}+36783\right ) \sqrt {x^{4}+3 x^{2}+2}}{1155} \]
command
Integrate[(7 + 5*x^2)^2*(2 + 3*x^2 + x^4)^(3/2),x]
Mathematica 13.1 output
\[ \frac {429318 x+1160065 x^3+1333551 x^5+892084 x^7+363480 x^9+82075 x^{11}+7875 x^{13}-171402 i \sqrt {1+x^2} \sqrt {2+x^2} E\left (\left .i \sinh ^{-1}\left (\frac {x}{\sqrt {2}}\right )\right |2\right )-78420 i \sqrt {1+x^2} \sqrt {2+x^2} F\left (\left .i \sinh ^{-1}\left (\frac {x}{\sqrt {2}}\right )\right |2\right )}{3465 \sqrt {2+3 x^2+x^4}} \]
Mathematica 12.3 output
\[ \text {\$Aborted} \]________________________________________________________________________________________