Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 426: 61

Answer

$$\ln \left| {\ln x} \right| + C$$

Work Step by Step

$$\eqalign{ & \int {\frac{{dx}}{{x\ln x}}} ,{\text{ with }}u = \ln x,{\text{ }}du = \frac{{dx}}{x} \cr & {\text{using the indicated substitution}} \cr & \int {\frac{{dx}}{{x\ln x}}} = \int {\frac{1}{u}du} \cr & {\text{integrating}} \cr & = \ln \left| u \right| + C \cr & {\text{Back substitute }}u = \ln x \cr & = \ln \left| {\ln x} \right| + C \cr} $$
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