converge/diverge integral I need to tell if this integral converge or diverge: $\int_0^{\infty}\frac{1}{x^{1-\frac{1}{x}}}dx$.Now, I think this diverge because $\int_0^{\infty}\frac{1}{x}dx$ diverge because $\frac{1}{x^{a}}$ diverge for a<=1. Can you help me, thanks.

**Hint**. Observe that, for $x\geq1$, you have $$ \frac1{x^{1-1/x}}\geq \frac{1}{x} $$ giving, for $M\geq1$, $$ \int_1^M\frac1{x^{1-1/x}}\:dx\geq \int_1^M\frac1x\:dx $$ then conclude easily.