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 - Page 446: 71


$\int \frac{(logx)^{2}}{x}dx=\frac{(lnx)^{3}}{3}+ Constant$

Work Step by Step

Evaluate $\int \frac{(logx)^{2}}{x}dx$. Consider $ln x =t$ and $\frac{1}{x} dx = dt$ Thus, $\int \frac{(logx)^{2}}{x}dx=\int t^{2} dt$ $=\frac{t^{3}}{3}+ Constant$ $=\frac{(lnx)^{3}}{3}+ Constant$ Hence, $\int \frac{(logx)^{2}}{x}dx=\frac{(lnx)^{3}}{3}+ Constant$
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