Determine $\mathbb{E}[X]$ with known pdf $f(x)$

Question

Say we have probability density function $$f(x) = \frac{a}{(x+a)^2}.$$ Here $a>0$ and $x\geq 0$. I've already checked that $\int_0^\infty f(x) = 1$. However I've trouble determining the expected value. I know that: $$\mathbb{E}[X] = \int_0^\infty x\ f(x)\ \text{d}x,$$ however Wolfram says that this intergral does not converge. Is there something wrong with the pdf? Or is there another way to get the expectation? Is it possible that a well define pdf has no expectation?