Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 97

Answer

$$\frac{1}{3}(\ln x)^3+c.$$

Work Step by Step

Let $ u=\ln x $, then $ du= \frac{1}{x} dx $ and hence $$\int \frac{(\ln x)^2 }{x}dx = \int u^2du=\frac{1}{3}u^3+c\\ =\frac{1}{3}(\ln x)^3+c.$$
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