Comparison test for ${{{\int_{{1}}^{{\infty}}\frac{1-e^{-x}}{x}}\,{d}{x}}}$

Question

Using the comparison test determine whether the following integral will converge.

$$\displaystyle{{{\int_{{1}}^{{\infty}}\frac{1-e^{-x}}{x}}\,{d}{x}}}$$

I've struggled with this for a good while now... Any tips on how to proceed?

Answer 1

$\frac {1 -e^{-x}} x \geq \frac 1 x -\frac 1 {x^{2}} \geq \frac 1 {2x}$ for $x >2$.