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

$\displaystyle

\int\frac{x^2+2x}{(x^2+4)^2}~dx

$

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

$\displaystyle

-4\int\frac{1}{(x^2+4)^2}~dx

$

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:

$\displaystyle

-4\bigg(\frac{x}{8(x^2+4)}+\frac{1}{16}arctan\bigg[\frac{x}{2}\bigg]\bigg)

$

I'm in a 5 week Calc2 course and I feel like this guy -->

after just the first week.