Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise: 50

Answer

$\int \frac{2^{x}}{2^{x}+1}dx=\frac{1}{ln2}ln|2^{x}+1|+C$

Work Step by Step

Evaluate the integral $\int \frac{2^{x}}{2^{x}+1}dx$ Consider $2^{x}=t$ and $dx=\frac{dt}{2^{x}ln2}$ Now, $\int \frac{2^{x}}{2^{x}+1}dx=\frac{1}{ln2}\int\frac{dt}{t+1}$ $=\frac{1}{ln2}ln|t+1|+C$ Hence, $\int \frac{2^{x}}{2^{x}+1}dx=\frac{1}{ln2}ln|2^{x}+1|+C$
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