# Evaluating $\int \frac{x+1}{(x^2+2)^2}\, dx$ by choosing an appropriate contour in the upper half plane

How do you solve this question?

Evaluate: $\int \frac{x+1}{(x^2+2)^2}\, dx$ by choosing an appropriate contour in the upper half plane

How would the answer change if this question was evaluated with the lower half plane instead of the upper half.

And how do you give an alternative method for deducing the behaviour of the integral as the contour tends to infinity.

• I think you probably want to include limits of integration if you want to use the contour integration method, and given the fact that you ask about the behaviour as the contour as it “tends to infinity” (I presume the limits should be $-\infty$ to $\infty$). – John Don Dec 14 '17 at 8:27
• It seems to be a suggestion for a change of variable of the kind $y=f(x)>0$. – gimusi Dec 14 '17 at 8:27