I have a homework question that I found a little tricky. I ended up getting an answer but I was hoping for some verification, because I don't feel like I did it correctly. My answer is based on an online integrator, and I know this paper is a bit scattered and difficult to make sense of, so the original equation is on top, the factored version is below the denominator, I did u-substitution to double-check under that, changed it to fractions, and solved for A and B then my answer is on the last line.
Also, if it turns out my answer is correct, I'm a tiny bit confused on how the online integrator got such an answer for both separate integrals and a short explanation of how it ended up being that answer would be great. Any help in general is appreciated, I've been stuck on this problem for two days now so it'd be great to knock it out finally.