$\displaystyle X$ is a standard normal random variable. Show that the PDF of $\displaystyle Z=(X+1)^2$ is

$\displaystyle (8\pi z)^{-\frac{1}{2}}e^{-\frac{1}{2}(z+1)}\left(e^{\sqrt{z}}+e^{-\sqrt{z}}\right)$

I've tried thisloadsof times but I can't get anywhere near the answer