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: 16


$-\dfrac {1}{\ln x}+c$

Work Step by Step

$v=\ln x\Rightarrow dv=\dfrac {1}{x}dx$ $$\Rightarrow \int \dfrac {1}{x\left( \ln x\right) ^{2}}dx=\int \dfrac {1}{\left( \ln x\right) ^{2}}\times \dfrac {1}{x}dx=\int \dfrac {1}{v^{2}}dv=\int v^{-2}dv=-v^{-1}+c=-({\ln x})^{-1}+c=-\dfrac {1}{\ln x}+c$$
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