Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 409: 18


$$\int\frac{\sin 2x}{\sin x}dx=2\sin x+C$$

Work Step by Step

$$A=\int\frac{\sin 2x}{\sin x}dx$$ $$A=\int\frac{2\sin x\cos x}{\sin x}dx$$ $$A=\int2\cos xdx$$ From Table 1, $$\int cf(x)dx=c\int f(x)dx$$ Therefore, $$A=2\int\cos xdx$$ From Table 1, we also get $$\int(\cos x)dx=\sin x+C$$ Therefore, $$A=2\sin x+C$$
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