How to compute the following integral

[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

 

[d_leet]

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

 

[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...

 

[courtrigrad]

use integration by parts after making the substitution.

 

[thenewbosco]

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

 

[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.

 

[thenewbosco]

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

 

[dextercioby]

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

Daniel.