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: 16


a) $-\cot x+C$ b) $\cot (\dfrac{3x}{2})+C$ c) $x+4 \cot 2x+C$

Work Step by Step

a) The anti-derivative for $csc^2 x$ is $-\cot x+C$ b) The anti-derivative is: $\dfrac{-3}{2}(-\dfrac{1}{3/2} cot (\dfrac{3x}{2}))= \cot (\dfrac{3x}{2})+C$ c) The anti-derivative is: $x-8(\dfrac{-1}{2} \cot 2x)=x+4 \cot 2x+C$
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