Partial Fraction Integral

Here's the problem, I keep getting stuck on one part...

After separating into 2 integrals and taking the partial fraction of the first part, I end up getting stuck on the following integral:

My question at this point: what's my substitution? I'm not seeing it but know, based on form, that it has something to do with arctan. I picked up the answer from the Mathematica Integrator but need to know the steps.

The answer is apparently:

I'm in a 5 week Calc2 course and I feel like this guy --> (Headbang) after just the first week.