Calculus (3rd Edition)

Published by W. H. Freeman

Chapter 8 - Techniques of Integration - 8.6 Strategies for Integration - Exercises - Page 431: 27

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*}

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