Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 4 - Integration - 4.2 The Indefinite Integral - Exercises Set 4.2 - Page 279: 27


$$\sec x + C$$

Work Step by Step

$$\eqalign{ & \int {\frac{{\sin x}}{{{{\cos }^2}x}}} dx \cr & {\text{write the denominator as a product}} \cr & \int {\frac{{\sin x}}{{{{\cos }^2}x}}} dx = \int {\left( {\frac{{\sin x}}{{\cos x}}} \right)\left( {\frac{1}{{\cos x}}} \right)} dx \cr & {\text{basic trigonometric identities }}\tan x = \frac{{\sin x}}{{\cos x}}{\text{ and }}\sec x = \frac{1}{{\cos x}} \cr & = \int {\tan x\sec x} dx \cr & {\text{use integration formula from table 4}}{\text{.2}}{\text{.1}} \cr & = \sec x + C \cr} $$
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