You will need the covariance divided by the st. deviations.

The covariance is since E(Z)=0.

Now

since Z is symmetric and the odd moments should be zero.

Next and

Then

Where you will need .

That's most of this problem. You should not even consider integrating it, whatsoever.

Fine, no one's going to finish this... .

I was too lazy to compute that fourth moment, so I looked it up at http://en.wikipedia.org/wiki/Normal_distribution

It's 3, so .

This seems to be (or not 2b, that is your question) .