Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 6 - Applications of Integration - 6.8 Logarithmic and Exponential - 6.8 Exercises: 18


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

Work Step by Step

$$\eqalign{ & \int {\frac{{dx}}{{x\ln x\ln \left( {\ln x} \right)}}} \cr & {\text{substitute }}u = \ln \left( {\ln x} \right),{\text{ }}du = \frac{{1/x}}{{\ln x}}dx \cr & du = \frac{1}{{x\ln x}} \cr & \int {\frac{{dx}}{{x\ln x\ln \left( {\ln x} \right)}}} = \int {\frac{1}{u}du} \cr & = \int {\frac{1}{u}} du \cr & {\text{find the antiderivative}} \cr & = \ln \left| u \right| + C \cr & {\text{replace }}u = \ln \left( {\ln x} \right) \cr & = \ln \left| {\ln \left( {\ln x} \right)} \right| + C \cr} $$
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