Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 13 - Section 13.1 - The Indefinite Integral - Exercises - Page 958: 22

Answer

$-2x^{-1}+\displaystyle \frac{1}{12}\cdot x^{3}+C$

Work Step by Step

Written in exponent form, applying Sum and Difference RuIes, ...$=\displaystyle \int 2u^{-2}du+\displaystyle \int(\frac{1}{4}u^{2})du$ ... Constant MultipIe Rule $=2\displaystyle \int u^{-2}du+\frac{1}{4}\int u^{2}du$ ... Power Rule, both: $( n\neq-1)$ $=2\displaystyle \cdot\frac{x^{-2+1}}{-2+1}+\frac{1}{4}\cdot\frac{x^{2+1}}{2+1}+C$ $=-2x^{-1}+\displaystyle \frac{1}{12}\cdot x^{3}+C$
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