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: 87


$$ \int \frac{ d x}{2x+4} =\frac{1}{2}\ln |2x+4|+c. $$

Work Step by Step

Let $ u=2x+4$ and hence $ du=2dx $, then we have $$ \int \frac{ d x}{2x+4}=\frac{1}{2}\int \frac{ d u}{u}= \frac{1}{2}\ln |u|+c=\frac{1}{2}\ln |2x+4|+c. $$
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