University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.2 - Trigonometric Integrals - Exercises - Page 435: 51


$-\frac{1}{2}cos x -\frac{1}{10}cos 5x +C$

Work Step by Step

Applying the product-to-sum identity, we have $\int sin 3x cos 2xdx=\int\frac{1}{2}(sinx+sin5x)dx$ $= \frac{1}{2}\int sinxdx + \frac{1}{2}\int sin 5xdx$ $=\frac{1}{2}\times-cosx + \frac{1}{2}\times\frac{-cos5x}{5}+C$ $= -\frac{1}{2}cos x -\frac{1}{10}cos 5x +C$
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