Find E(X^-1) for stochastic variable

Question

Let $X$ be a stochastic variable with density function: $f(x)=x\exp(-x)$ if $x>0$ and $0$ otherwise.

Show that $E(X^{-1} )=1$.

I believe I have to integrate but is it simple $x\exp(-x)$ I integrate?

Answer 1

If $X$ has density $f(x)$, $\mathbb E[g(X)] = \int_R g(x) f(x)\; dx$.