Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 387: 61


$$\int \frac{(\ln x)^2}{x}dx =\frac{1}{3}(\ln x)^3+c.$$

Work Step by Step

Since $ u=\ln x $, then $ du= \frac{dx}{x}$ 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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