# Complex analysis

1. Feb 28, 2009

### asi123

1. The problem statement, all variables and given/known data

Hey guys.

So, I need to calculate this integral. I uploaded what I tried to do.
First of all, did the substitute, then I tried to use the residue theorem so I was looking for the residue of z=0 which is happen to be a removable singular point so it's just 0, then I went for the z=2*pi*k (when k can't be 0) residue and found out that it's 0.
I guess I have a mistake there, any idea guys?

Thanks.

2. Relevant equations

3. The attempt at a solution

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2. Mar 1, 2009

### gabbagabbahey

Your substitutions a little fishy; does $$e^{z}=x^2+1$$ really mean that $$x=\sqrt{e^z-1}$$? How are you excluding the negative root?

3. Mar 1, 2009

### HallsofIvy

If you are going to use residues, what close path are you going to integrate over?

4. Mar 1, 2009

### asi123

I thought about a closed contour consisting of the semi-circle with radius r and centre at z = 0 and the line segment going from z = -r to z = r and then doing the r --> oo thing. That way, I'll only have one pole, p=i.
Then, I'll try to break it into -r to 0 and from 0 to r, and find the latter, does that seems right?

Thanks.