Answer
Diverges
Work Step by Step
Apply a direct comparison test.
We can see that $0 \leq \dfrac{e}{x} \leq \dfrac{e^x}{x}$
And $\int_{1}^{\infty} \dfrac{e dx}{x}=\lim\limits_{p \to \infty}\int_{1}^{p}\dfrac{e dx}{x}$
and $\lim\limits_{p \to \infty}\int_{1}^{p}\dfrac{e dx}{x}=\lim\limits_{p \to \infty}[e \ln |x|]_{1}^{p}=\infty$
Hence, the given integral diverges by the direct comparison test.