Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 109



Work Step by Step

Using the fact that $\frac{u'}{u}=\ln u $, we have $$\int_2^{4} \frac{1}{3t+4}dt=\frac{1}{3}\int_2^{4} \frac{3}{3t+4}dt=\frac{1}{3}\ln (3t+4)|_2^{4}\\ =\frac{1}{3}(\ln 16-\ln 10)=\frac{1}{3}\ln \frac{16}{10}=\frac{1}{3}\ln\frac{8}{5}. $$ where used the property: $\ln A-\ln B=\frac{A}{B}$.
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