$\lim_{n\rightarrow +\infty}\int_{-\infty}^{+\infty}n\log\left(1+\bigg[\frac {f(x)} n \bigg]^\alpha\right)\ dx$ where $f$ is an integrable function

Question

Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a Riemann-integrable function on $\mathbb{R}$ such that

$$f(x) \geq 0 \ \ \forall \ x \in \mathbb{R} \ \ \text{ and } \int_{-\infty}^{+\infty} f > 0 .$$ Calculate, based on the value of $\alpha$, $$\lim_{n\rightarrow +\infty}\int_{-\infty}^{+\infty}n\log\left(1+\bigg[\frac {f(x)} n \bigg]^\alpha\right)\ dx,$$ where $\alpha \in (0, +\infty)$. I have to use the Lebesgue measure, and the monotone convergence theorem, but I can't figure how to based on the value of $\alpha$.