mean of continuous random variable

This is really a calculus question, but is part of a probability problem. Apologies if I've posted in the wrong place.

I'm given a cumulative distribution function $\displaystyle F(x)=1-(x+1)^{-2}, x>0$ and 0 elsewhere. I use this to find the probability density function and then evaluate $\displaystyle P\{1<X<3\}$, and I'm okay through all this.

When I go to calculate the mean, $\displaystyle E[X]=\int_{-\infty}^{\infty}xp(x)\,dx=\int_{0}^{\infty}xp(x)\, dx$, I get a $\displaystyle ln(0)$ in the final step of the evaluation. Where'd I go wrong?