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: 66

Answer

$\int_0^3\frac{dx}{5x+1}=\frac{4}{5}ln2$

Work Step by Step

Evaluate the integral $\int_0^3\frac{dx}{5x+1}$. $\int_0^3\frac{dx}{5x+1}=ln[\frac{5x+1}{5}]_0^3$ $=\frac{1}{5}[ln16-ln1]$ $=\frac{1}{5}[ln 2^{4}-ln1]$ Since $ln 1= 0$ Thus, $=\frac{1}{5}[ln 2^{4}-0]=\frac{1}{5}[ln 2^{4}]$ Hence, $\int_0^3\frac{dx}{5x+1}=\frac{4}{5}ln2$
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