I'm stuck with something that I think should be straightforward but can't see what to do.

I'm trying to find where ~N( , ). I know that this is i.e. the integral of the inner product of and the pdf of the Normal distribution. This is where it falls apart - how do I integrate this? I think it's done by substitution when dealing with with the standard normal but this has the extra exponential and I'm not sure how to do it.

Help appreciated, thanks.