Hint:
$\displaystyle \displaystyle \int_{-\infty}^{\infty} \frac{1}{\sqrt{2 \pi}} z^2e^{-z^2/2}$
Rewrite this as
$\displaystyle \displaystyle \int_{-\infty}^{\infty} \frac{1}{\sqrt{2 \pi}} z \cdot ze^{-z^2/2}$
Integration by parts:
$\displaystyle \displaystyle \int p dq = pq - \int q dp$
Use $\displaystyle \displaystyle p = z$ and $\displaystyle \displaystyle dq = ze^{-z^2/2}dz$
-Dan
Since you have the first, for the second my suggestion is to set p = z^3 and dq the same as in the first part.