# How do you integrate this function (not by parts)?

1. Oct 6, 2011

### zheng89120

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

integrate: r2*exp(i*k*r - r2/a2) from -infinity to +infinity (in terms of r)

2. Relevant equations

relevant integration table

3. The attempt at a solution

not sure what this function or the method to solve this function is called

Last edited: Oct 6, 2011
2. Oct 6, 2011

### Mute

I would start by completing the square in the exponential, and then changing variables to y = r - b, where b is whatever you get when you complete the square. Then, use know results for the integrals of Gaussian functions.

3. Oct 6, 2011

### CompuChip

Without going through the whole exercise, the thing that comes to mind is splitting off a square. I think that eventually you will find a substitution like $z = r/a - \tfrac12 i a k$ which will allow you to write it in terms of integrals like
$\int e^{z^2}$ and $\int z e^{z^2}$
which you can do without partial integration.