I'm not good at this kind of topics, but I'm trying to solve a problem for the theory of probabilities - I need to find a continuous PDF, which limit at $+\infty$ doesn't exist - so I came across this function, which is represented graphically.
Here's 
Its integral is equal to 1. It's supposed to be a probability density function. I need to know the expected value (or the mean) for it: $\int_{-\infty}^{+\infty}xf_{\xi}(x)dx$. I don't have to actually perform any calculations, but I must prove that it's possible, or, in other words, that $\int_{-\infty}^{+\infty}|x|f_{\xi}(x)dx < \infty$
How do I go about that? Is there any way to approximate this function analitically? (but its integral must be 1 in any case). I would appreciate any help!