Finding mean and variance of RV

Hello everyone,

The question asks to find the mean and variance of X = (1-Z)^(-1/2) where Z is randomly selected from [0,1].

Also recommends using a formula $\displaystyle {E}(x) = \int_{0} ^ \infty (1- Fx(t)) \,{d}t$

I found the pdf $\displaystyle fx(x) = 2/x^3$ for x= [1,infinity) and cdf $\displaystyle F(x)= 1-1/x^2$

Calculating $\displaystyle {E}(X) = \int_{-\infty}^\infty x f(x)\, {d}x $ from here gives me an answer of 2. While the previous formula that uses CDF gives a different answer. Also I'm not sure how to find the second moment E(x^2), because it does not converge.

Any input on what I could be doing wrong is appreciated.

Thank you