1. ## Integral of (x+3)/(x^2+4)

Integral of (x+3)/(x^2+4)

I'm trying to do it by parts:

u = x+3 du = 1
dv = 1/(x^2+4) v = 1/2 arctan (x/2)

but, I'm not sure this is the right way. It gets a bit messy and I assume I'm doing something wrong.

2. We may use the fact that

$\frac{x+3}{x^2+4}=\frac{x}{x^2+4}+\frac{3}{x^2+4}.$