# Complex integral

1. Nov 21, 2013

### aaaa202

1. The problem statement, all variables and given/known data
I have an integral of the form:

0exp(ax+ibx)/x dx
What is the general method for solving an integral of this kind.

2. Relevant equations
Maybe residual calculus?

3. The attempt at a solution

2. Nov 21, 2013

### brmath

Residues sound like the only way. However, make sure you are using $e^{-z}/z$; with a positive exponent your integral will not converge.

3. Nov 21, 2013

### Dick

I don't see how it's going to converge no matter what a is. It's also divergent near x=0.

4. Nov 21, 2013

### brmath

So true. Wish I had read the lower limit as 0 instead of 1. Can I blame it on bad eyesight?

5. Nov 22, 2013

### aaaa202

I need it to converge badly. But I know what mistake I made. I wanted the integral to be the imaginary part of the above. At least I think so. I have attached the whole exercise now as pdf. Is it correct what I have done so far and how do I evaluate the integral?

#### Attached Files:

• ###### FT.pdf
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Last edited: Nov 22, 2013
6. Nov 22, 2013

### Ray Vickson

It all looks incorrect. You wanted to integrate something like $\exp(-cr)/r \, \exp(ikr\ cos(\theta))$ over $R^3$ in spherical corrdinates. The volume element in spherical coordinates is not $dr \, d\theta \, d\phi$; it is $r^2 \sin(\theta)\, dr \, d \theta \, d \phi$.

7. Nov 23, 2013

### aaaa202

Right, I wrote that in a rush I can see. So basically I forgot the sin(theta) in the first line but it should be there or I couldnt make the substitution dcos(theta). Also the r^2 should be there and 1/r I forgot too so I would end up with having to integrate the imaginary part of r times the expression on the last line. But still with that, I don't see how I can solve that integral.

8. Nov 23, 2013

### Ray Vickson

Your final integral is "elementary" and is the type of thing you learned to do in Calculus 101. Look at it again.

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