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 280: 63

Answer

$\tan x - x + C$

Work Step by Step

$$\eqalign{ & \int {{{\tan }^2}x} dx \cr & {\text{using the pythagorean identity }}{\tan ^2}x + 1 = {\sec ^2}x \cr & {\text{then}}{\text{, }}{\tan ^2}x = {\sec ^2}x - 1 \cr & \int {{{\tan }^2}x} dx = \int {\left( {{{\sec }^2}x - 1} \right)} dx \cr & {\text{sum and difference rule for the integrand}} \cr & \int {{{\sec }^2}x} dx - \int {dx} \cr & {\text{using the integration basic rules}} \cr & \tan x - x + C \cr} $$
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