this can be done.
Notice that then v=
You will then notice that the uv term of the integration by parts is 0 (remember that for definite integrals, this term gets evaluated at the main integral's bounds, i.e., and 0.) What you're left with is
A rather cool method for that one will use polar coordinates. here's a link:
Gaussian integral - Wikipedia, the free encyclopedia
(note the limits of integration for the Gaussian integral: You will need to divide by 2 (justified as the integrand is an even function)).