## Calculus 10th Edition

Published by Brooks Cole

# Chapter 4 - Integration - 4.1 Exercises: 16

#### Answer

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

#### Work Step by Step

$\int (\sqrt x + \frac{1}{2\sqrt x})dx$ = $\int \sqrt x dx + \int\frac{1}{2\sqrt x}dx$ = $\int x^{\frac{1}{2}} dx + \int\frac{1}{2}\frac{1}{\sqrt x}dx$ =$\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1} + C' + \frac{1}{2}\int x^{-\frac{1}{2}}dx$ = $\frac{x^{\frac{3}{2}}}{\frac{3}{2}} + \frac{1}{2}(\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}) + C$ = $\frac{2x^{\frac{3}{2}}}{3} + \frac{1}{2}(\frac{x^{\frac{1}{2}}}{\frac{1}{2}}) + C$ = $\frac{2x^{\frac{3}{2}}}{3} + \frac{1}{2}(\frac{2x^{\frac{1}{2}}}{1}) + C$ = $\frac{2}{3}x^{\frac{3}{2}} + \frac{2}{2}x^{\frac{1}{2}} + C$ = $\frac{2}{3}x^{\frac{3}{2}} + x^{\frac{1}{2}} + C$ The result can be checked by differentiating, and it works.

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