Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - 7.2 Substitution - 7.2 Exercises: 32

Answer

\[\ln \left| {\ln x} \right| + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{1}{{x\,\left( {\ln x} \right)}}dx} \hfill \\ Set\,\,u = \ln x\,\,,\,So\,\,that\,\,du = \frac{1}{x}dx \hfill \\ Then \hfill \\ \int_{}^{} {\frac{1}{{x\,\left( {\ln x} \right)}}dx} = \int_{}^{} {\frac{1}{u}du} \hfill \\ Integrating \hfill \\ \ln \left| u \right| + C \hfill \\ Substituting\,\,u = \ln x\,\,gives \hfill \\ \ln \left| {\ln x} \right| + C \hfill \\ \end{gathered} \]
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