# How to compute the following integral

1. Nov 20, 2006

### thenewbosco

I was wondering how to compute the following integral:
$$\int xe^{\frac{-x^2+2x\cdot x_0-x_{0}^2}{2a^2}}dx$$

it would be quite simple if there was no term in the exponent x times x0 i think...any help on this thanks

2. Nov 20, 2006

### d_leet

Factor the expression in the exponent and then make a substitution.

3. Nov 20, 2006

### thenewbosco

i factored the exponent to be -(x-x0)^2 but what is the substitution to make? u = x-xo? this does not help because of the x...

4. Nov 20, 2006

use integration by parts after making the substitution.

5. Nov 20, 2006

### thenewbosco

so the substitution i proposed is the correct one to make?

6. Nov 20, 2006

### d_leet

Try u=(x-x0)2, I think that should work, but it might be a bit messy, I'm pretty sure parts will not work though.

7. Nov 20, 2006

### thenewbosco

but for what you propose then du=2(x-xo)dx, which cannot be put into the integral like this...

8. Nov 21, 2006

### dextercioby

It has to have some error function in it, so definitely it's not an elementary integral.

Daniel.