Answer
$\frac{2}{3}sin^{3/2}x-\frac{2}{7}sin^{7/2}x+C$
Work Step by Step
Let u=$sin x=>du=cosxdx$
=$\int \sqrt{sinx}(1-sin^2x)cosxdx$
=$\int (u^{1/2}-u^{5/2})du$
=$\frac{2}{3}u^{3/2}-\frac{2}{7}u^{7/2}+C$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 5: Integrals - Section 5.5 - Indefinite Integrals and the Substitution Method - Exercises 5.5 - Page 295: 22
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