Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 4 - Integration - 4.1 Exercises: 21

Answer

$=\frac{2}{3}x^{\frac{3}{2}} + 12x^{\frac{1}{2}} + C$

Work Step by Step

$\int (\frac{x+6}{\sqrt {x}})dx$ $\int (\frac{x}{x^{\frac{1}{2}}} + \frac{6}{\sqrt {x}})dx$ $\int (x^{1-\frac{1}{2}}) + 6x^{-\frac{1}{2}}dx$ $\int (x^{\frac{1}{2}}) + 6x^{-\frac{1}{2}}dx$ $= \frac{x^{\frac{3}{2}}}{\frac{3}{2}} + \frac{6x^{\frac{1}{2}}}{\frac{1}{2}} + C$ $= (x^{\frac{3}{2}} \times \frac{2}{3}) + (6x^{\frac{1}{2}} \times 2) + C$ $=\frac{2}{3}x^{\frac{3}{2}} + 12x^{\frac{1}{2}} + C$
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