First you should recognise from the joint pdf that and .

Therefore . Mr F Edit: The mistake I mention below is here. See post #3.

Note: .

So the task is to calculate :

Now complete the square and re-arrange:

where is the pdf of .

Now note that represents and so:

.

Therefore:

where the moments are for a standard normal distribution. Cheating and refering to a table of moments (see Normal distribution - Wikipedia, the free encyclopedia):

.

Therefore .

This is different from the result that was given to be proved so there's a mistake somewhere (that I don't have time to look for). Nevertheless, I'm sure you get the idea.