Let $X$ be Gamma distributed with density $$f_\theta(x)=\frac{\theta^3}{2}x^2e^{-\theta x},\quad\theta\in(0,\infty).$$
Now I want to calculate $E[|X|]$, i.e.
$$\int_{-\infty}^\infty|x|\frac{\theta^3}{2}x^2e^{-\theta x}dx,$$
but I do not really know how. In the end I just want to know if it is $<\infty$. Is there an easy argument?