Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises: 90

Answer

$\frac{(4+e^x)^6}{6}+C$

Work Step by Step

Let $u=4+e^x$. Then $du=e^xdx$. $\int e^x(4+e^x)^5 dx$ $=\int (4+e^x)^5e^x dx$ $=\int u^5 du$ $=\frac{u^6}{6}+C$ $=\frac{(4+e^x)^6}{6}+C$
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