Answer
$$-\ln |e^{-x}+1|+C$$
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*}
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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