What is the expectation of $\frac{1}{X}$ for exponential distribution?

Question

I was trying to solve the following question: What is the expectation of $\frac{1}{X}$ for exponential distribution? Is $\frac{1}{X}$ unbiased estimator for $\lambda$. As the distribution function for exponential distribution is given by, $$ f(x)=\lambda e^{-\lambda x},\ \ x>0,\ \lambda>0. $$ $$ E\left[\frac{1}{X}\right]=\int_0^\infty \frac{1}{x}f(x)=\int_0^\infty \frac{1}{x}\lambda e^{-\lambda x} $$ Now, I stuck in evaluating the integral. How to integrate this or is there any other method for computing the expectation value.