Answer
$\int(1-x)e^xdx=2e^x-xe^x+C$
Work Step by Step
We integrate as follows:
$u=1-x$
$D(u)=-1$
$v=e^x$
$I(v)=e^x$
$\int u·v~dx=u·I(v)-\int D(u)I(v)dx$
$\int(1-x)e^xdx=(1-x)e^x-\int-1e^xdx=e^x-xe^x+\int e^xdx=e^x-xe^x+e^x+C=2e^x-xe^x+C$
Finite Math and Applied Calculus (6th Edition)
by Waner, Stefan; Costenoble, Steven
Published by
Brooks Cole
ISBN 10:
1133607705
ISBN 13:
978-1-13360-770-0
Chapter 14 - Section 14.1 - Integration by Parts - Exercises - Page 1021: 4
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