Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 4 - Integration - 4.5 Exercises - Page 302: 50

Answer

$-2(2-x)^{\frac{3}{2}} + \frac{2}{5}(2-x)^{\frac{5}{2}} +C$

Work Step by Step

Find the indefinite integral Let $u=2-x$, $du= -dx$, $x=2-u$ $\int (x+1)\sqrt {2-x} dx$, Substitute $-\int (3-u)u^{\frac{1}{2}}du$ $-\int(3u^{\frac{1}{2}} - u^{\frac{3}{2}})du$, Integrate $-2u^{\frac{3}{2}} + \frac{2}{5}u^{\frac{5}{2}} +C$ $-2(2-x)^{\frac{3}{2}} + \frac{2}{5}(2-x)^{\frac{5}{2}} +C$
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