University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Section 4.8 - Antiderivatives - Exercises - Page 271: 15


a) $\tan x$ b) $2 \tan (\dfrac{x}{3})+C$ c) $\dfrac{-2}{3} \tan (\dfrac{3x}{2})+C$

Work Step by Step

a) The anti-derivative for $sec^2 x$ is $\tan x$ b) The anti-derivative is: $\dfrac{2}{3}sec^2 (\dfrac{x}{3})=2 \tan (\dfrac{x}{3})+C$ c) The anti-derivative is: $-sec^2 (\dfrac{3x}{2}=\dfrac{-2}{3} \tan (\dfrac{3x}{2})+C$
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