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: 22


a) $\frac{x^{\sqrt {3}+1}}{\sqrt {3}+1}+C$ b) $\frac{x^{\pi+1}}{\pi+1}+C$ c) $\frac{x^{\sqrt 2}}{\sqrt 2}+C$

Work Step by Step

Recall: $\int x^{n}dx=\frac{x^{n+1}}{n+1}$ Use this formula to obtain the results below: a) $\int x^{\sqrt 3}dx=\frac{x^{\sqrt {3}+1}}{\sqrt {3}+1}+C$ b) $\int x^{\pi}dx=\frac{x^{\pi+1}}{\pi+1}+C $ c) $\int x^{\sqrt {2}-1}dx=\frac{x^{(\sqrt {2}-1)+1}}{(\sqrt {2}-1)+1}+C=\frac{x^{\sqrt 2}}{\sqrt 2}+C $
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