Answer
$\frac{2}{3}(1-e^x)^{\frac{3}{2}}+C$
Work Step by Step
$\int (e^x)(\sqrt{1-e^x})dx$
let $ 1-e^x=u$
$-e^{x}$ $dx=du$
$\int (e^x)(\sqrt{1-e^x})dx$
$=-\frac{2}{3}u^{\frac{3}{2}}+C$
$=\frac{2}{3}(1-e^x)^{\frac{3}{2}}+C$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.4 Exercises - Page 354: 101
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