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: 4


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

Work Step by Step

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