Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4 Derivatives of Logarithmic Functions - 6.4 Exercises: 77

Answer

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

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, $\int \frac{(logx)^{2}}{x}dx=\frac{(lnx)^{3}}{3}+ Constant$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.