Doing this problem. I have the antiderivative after using partial fraction decomposition. What I do not understand is the answer. I thought that this was divergent, but it is convergent. When I look at the end product, I do not get how that converges.

Problem:

50. $\displaystyle \int^2_\infty \frac{dx}{(x+3)(x+1)^2}$

Answer:

Now my question is, as lim R-> $\displaystyle \infty-$, does that cancel out the "ln" terms?