For wich $\alpha > 0$ and $\beta \in \mathbb{R}$ is $f: (1,\infty)\to \mathbb{R}: f(x)=\frac{(\ln(x))^\alpha}{(x-1)^\beta}$ Lebesgue integrable?

Question

I'm trying to search for wich $\alpha > 0$ and $\beta \in \mathbb{R}$ the function $f: (1,+\infty)\to \mathbb{R}: f(x)=\frac{(\ln(x))^\alpha}{(x-1)^\beta}$ becomes Lebesgue integrable, but I don't immediately see the restrictions I have to put on $\alpha$ and $\beta$. Can someone help me? Thank you in advance.