Does $\int^1_0\frac{(1-s)^\alpha}{s^\beta} \operatorname d \!s$ converge? I want to ask about the finitess of the following integral
\begin{equation}
\int^1_0\frac{(1-s)^\alpha}{s^\beta}ds
\end{equation}
when $\alpha>\beta>1$. This integral is very similar to the Beta function, aside from the negative power $-\beta$ here. Can anyone confirm if there really exists some big $\alpha$ such that the integral is finite? Thank you.

The integral is finite if and only if
$$\beta<1\quad\text{and}\quad -\alpha<1\iff \beta<1\quad\text{and}\quad \alpha>-1$$
