Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4 Derivatives of Logarithmic Functions - 6.4 Exercises: 80

Answer

$\int\frac{e^{x}}{e^{x}+1}dx=ln(e^{x}+1)+constant$

Work Step by Step

Evaluate $\int\frac{e^{x}}{e^{x}+1}dx$ Consider $e^{x}+1=t$ and $e^{x}dx=dt$ Thus, $\int\frac{e^{x}}{e^{x}+1}dx=\int \frac{dt}{t}$ $=ln|t|+constant$ $=ln(t)+constant$ Hence, $\int\frac{e^{x}}{e^{x}+1}dx=ln(e^{x}+1)+constant$
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