I've got the following question in a stats paper, just a bit stuck on how they get their answer:

Suppose that the random variable $\displaystyle X$ follows the exponential distribution $\displaystyle exp(\lambda)$, with p.d.f.

$\displaystyle f(x) = \lambda e^{-\lambda x}$ for $\displaystyle x > 0, \lambda > 0$, 0 otherwise.

Find the find the k-th moment of X, i.e. $\displaystyle E(X^k)$, for some positive integer $\displaystyle k$.

I know that this is $\displaystyle \int^{\infty}_0 \lambda x^k e^{-\lambda x}$, and also that the Gamma Distribution of $\displaystyle \Gamme(k + 1)$ is defined as $\displaystyle \int^{\infty}_0 x^k e^{-x}$, just not sure how to relate the two.

Thanks in advance for any help