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: 6

Answer

a) $\dfrac{1}{x^{2}}+C$ b) $\dfrac{-1}{4x^{2}}+C$ c) $\dfrac{x^4}{4}+\dfrac{1}{2x^{2}}+C$

Work Step by Step

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