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So I am taking a statistics course and finding this concept kinda challenging. wondering if someone can help me with the following problem!

Let X be a random variable with probability density function $$f(x)=\begin{cases}xe^{-x} \quad \text{if } x>0\\0 \quad \text{ } Otherwise.\end{cases} $$

we want to Determine the mgf of X whenever it exists.

I know that M(t) = E(e^(tx)) = integral of e^(tx)* f(x)

but not sure what to do from there.

Thanks for the help ^^