What values of p make \frac{1}{x^\alpha + x^\beta} integrable on (0,\infty)?

[AxiomOfChoice]

I'm working through some old prelim problems, and one of them has me stumped:

"For $0 < \alpha < \beta < \infty$, for which positive real numbers $p$ do we have

$$\frac{1}{x^\alpha + x^\beta} \in L^p (0,\infty)$$

 

[g_edgar]

Analyze separately how it behaves near 0 and near infinity.