how to determine if this integral converge or not?

Question

I should determine whether this is a convergent or divergent integral. The problem is that I don't know how to start. i need to use the comparison test but i don't know where to start. $$ \int_{0}^{1} \frac{e^{-x}}{x}dx $$

Answer 1

Since $e^{-x}$ is decreasing on $[0,1]$ and positive there, for $0\le x\le1$ you have $e^{-x}/x\ge e^{-1}/x$. Consequently, you can compare with the integral $\int_0^1 {dx\over e\cdot x}$ to show your integral diverges.