Answer
$\frac{(4+e^x)^6}{6}+C$
Work Step by Step
Let $u=4+e^x$. Then $du=e^xdx$.
$\int e^x(4+e^x)^5 dx$
$=\int (4+e^x)^5e^x dx$
$=\int u^5 du$
$=\frac{u^6}{6}+C$
$=\frac{(4+e^x)^6}{6}+C$
Calculus 8th Edition
by Stewart, James
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 - Page 454: 90
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