Convergence of $\int\frac{dx}{x^\alpha\log^\beta x}$ on $(0,1)$ and $(1,\infty)$

For what values of α and \(\beta\) the following integrals are convergent? (a) \(\int _ { 0 } ^ { 1 } { \frac { d x } { x ^ { \alpha } \log ^ { \beta } x } } ,\) (b) \(\int _ { 1 } ^ { \infty } { \frac { d x } { x ^ { \alpha } \log ^ { \beta } x } } .\)