Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.6 Strategies for Integration - Exercises - Page 431: 35


$$-\ln |e^{-x}+1|+C$$

Work Step by Step

\begin{align*} \int \frac{1}{1+e^{x}} d x&=\int \frac{1}{1+e^{x}} \frac{e^{-x}}{e^{-x}}d x\\ &=\int \frac{e^{-x}}{e^{-x}+1} d x\\ &=-\ln |e^{-x}+1|+C \end{align*}
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