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, $\int_e^6\frac{dx}{xlnx}=ln(ln6)$
Calculus 8th Edition
by Stewart, James
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 - Page 446: 70
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