Given pdfs $p(x), q(x)$, how can I show that the following integral exists? \begin{align*} \int_{-\infty}^{\infty} p(x)\log\left( \frac{p(x)}{q(x)}\right)dx \end{align*} where we follow the conventions from this answer.
I'm not sure how to approach this. I found this theorem on wikipedia, but it seems to not be very useful, since this function is not bounded, nor on a compact interval. Also, this function can take the value $\infty$.
If anyone could provide a resource for techniques on showing integrability, that would be greatly appreciated.