You will need the covariance divided by the st. deviations.
The covariance is since E(Z)=0.
since Z is symmetric and the odd moments should be zero.
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) .