Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 103


$$2(\ln x)^2+5\ln x+c$$

Work Step by Step

Using the facts that $\int du/u=\ln u$ and $\int udu=u^2/2$, we have $$\int \frac{4\ln x+5}{x}dx=\int \frac{4\ln x}{x} +\frac{5}{x}dx\\ =\int 4\ln x \ d(\ln x) +\int \frac{5}{x}dx \\ =2(\ln x)^2+5\ln x+c$$
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