Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises: 70

Answer

$\int_e^6\frac{dx}{xlnx}=ln(ln6)$

Work Step by Step

Consider $lnx=u$ and $\frac{1}{x}dx=du$ Thus, $\int_e^6\frac{dx}{xlnx}=\int_1^{ln6} \frac{du}{u}$ $=|lnu|_1^{ln6}$ $=|ln(ln6)-ln1|$ Hence, $\int_e^6\frac{dx}{xlnx}=ln(ln6)$
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