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 272: 36


$\dfrac{1}{3} x^{3/2}+4 x^{1/2} dx+C$

Work Step by Step

Given: $\int (\dfrac{\sqrt x}{2}+\dfrac{2}{\sqrt x}) dx$ or, $\int (\dfrac{\sqrt x}{2}+\dfrac{2}{\sqrt x}) dx=\int\dfrac{1}{2} x^{1/2}+2 x^{-1/2} dx$ We have: $\int x^n dx=\dfrac{x^{n+1}}{n+1}+C$ Thus, $\int\dfrac{1}{2} x^{1/2}+2 x^{-1/2} dx=\dfrac{1}{3} x^{3/2}+4 x^{1/2} dx+C$
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