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: 55


$\frac{sin x}{2}+\frac{sin 7x}{14}+C$

Work Step by Step

Applying product-to-sum identity, we get $\int cos 3xcos 4xdx= \int \frac{1}{2}(cos(-x)+cos 7x)dx$ $= \int \frac{1}{2}(cos x+ cos 7x)dx$ $=\frac{1}{2}\int cosxdx + \frac{1}{2}\int cos 7xdx$ $=\frac{1}{2}\times sin x+\frac{1}{2}\times\frac{sin 7x}{7}+C$ $=\frac{sin x}{2}+\frac{sin 7x}{14}+C$
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