I guess you’d factor into irreducible quadratics and do partial fractions, I’m pretty sure you can always integrate (Ax+B)/(Cx^2 + Dx + E)-looking stuff, though I forget how some of the cases work out
But yeah it looks pretty shitty; even some nested radicals as factors, I am curious how those show up. Not great
Wolfram solution for anyone wondering. Admittedly I'm not the best when it comes to solving complicated integrals in general and I'm a bit out of practice as well, so I can feel my brain melting just looking at it lol.