Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise: 47

Answer

$\int\frac{log_{10}x}{x}dx=\frac{x^{2}}{2ln10}$

Work Step by Step

Evaluate the integral $\int\frac{log_{10}x}{x}dx$ Apply Logarithmic base formula. $\int\frac{log_{10}x}{x}dx=\int\frac{lnx}{x(ln10)}$ Hence, $\int\frac{log_{10}x}{x}dx=\frac{x^{2}}{2ln10}$
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