Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition

Published by Brooks Cole
ISBN 10: 1-43904-957-2
ISBN 13: 978-1-43904-957-0

Chapter 5 - Accumulating Change: Limits of Sums and the Definite Integral - 5.9 Activities - Page 409: 10


$\dfrac {\left( \ln x\right) ^{5}}{5}+C$

Work Step by Step

$v=\ln x\Rightarrow dv=\dfrac {1}{x}dx$ $$\int \dfrac {\left( \ln x\right) ^{4}}{x}dx=\int \left( \ln x\right) ^{4}\times \dfrac {1}{x}dx=\int v^{4}dv=\dfrac {v^{5}}{5}+C=\dfrac {\left( \ln x\right) ^{5}}{5}+C$$
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