University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.7 - Improper Integrals - Exercises - Page 471: 58



Work Step by Step

Apply a direct comparison test. We can see that $0 \leq \dfrac{1}{x} \leq \dfrac{1}{\ln x}$ for all $x \gt 2$ And $\int_{2}^{\infty} \dfrac{dx}{\ln x}=\lim\limits_{p \to \infty}\int_{2}^{p} \dfrac{dx}{\ln x}$ and $\lim\limits_{p \to \infty}\int_{2}^{p} \dfrac{dx}{\ln x}=\infty$ Hence, the given integral diverges by the direct comparison test.
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