Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 6 - Applications of Integration - 6.8 Logarithmic and Exponential - 6.8 Exercises: 22

Answer

$${e^{\sin x}} + C$$

Work Step by Step

$$\eqalign{ & \int {\frac{{{e^{\sin x}}}}{{\sec x}}dx} \cr & {\text{use trigonometric identities}} \cr & = \int {{e^{\sin x}}\cos xdx} \cr & {\text{substitute }}u = \sin x,{\text{ }}du = \cos xdx \cr & = \int {{e^u}du} \cr & {\text{find the antiderivative}} \cr & = {e^u} + C \cr & {\text{replace }}u = \sin x \cr & = {e^{\sin x}} + C \cr} $$
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