Answer
$$\frac{1}{3}\ln |3e^{t}+1|+C$$
Work Step by Step
\begin{align*}
\int \frac{1}{3+e^{-t}} d t&=\int \frac{1}{3+e^{-t}} \frac{e^{t}}{e^{t}}d t\\
&=\int \frac{e^{t}}{3e^{t}+1} d x\\
&=\frac{1}{3}\ln |3e^{t}+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: 27
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