Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 336: 11


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

Work Step by Step

We can split the fraction into three different terms that can be simplified and are easier to take the integral of: $\int \frac{1 + \sqrt x + x}{\sqrt x} dx =\int( \frac{1}{\sqrt x} + \frac{\sqrt x}{\sqrt x} + \frac{x}{\sqrt x} )dx = \int (x^\frac{-1}{2} + 1 + x^\frac{1}{2}) dx$ We can now evaluate the integral, which results in $\frac {x^\frac{1}{2}}{\frac{1}{2}} + x + \frac {x^\frac{3}{2}}{\frac{3}{2}} + C $ which can be simplified further to $ 2x^\frac {1}{2} + x + \frac{2x^\frac{3}{2}}{3} + C$ *Note: Since it is an indefinite integral, we must include a general constant $C$ in our answer
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