## University Calculus: Early Transcendentals (3rd Edition)

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.