Answer
$\frac{1}{2}\sin^4 x$
Work Step by Step
$\int \sin^2 x\sin 2x\ dx$
$=\int \sin^2 x*2\sin x\cos x\ dx$
$=2\int\sin^3 x\cos x\ dx$
Let $u=\sin x$. Then $du=\cos x\ dx$.
$=2\int u^3\ du$
$=2*\frac{u^4}{4}$
$=\boxed{\frac{1}{2}\sin^4 x}$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 7 - Techniques of Integration - 7.2 Trigonometric Integrals - 7.2 Exercises - Page 524: 17
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