Calculus 8th Edition

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

Chapter 3 - Applications of Differentiation - 3.9 Antiderivatives - 3.9 Exercises - Page 282: 14


$$G(x)=-x^{-5}+2x^{-2}+2x +C$$

Work Step by Step

Given $$g(x) =\frac{5-4x^3+2x^6}{x^6}= 5x^{-6}-4x^{-3}+2$$ Then by using if $f(x)=x^{\alpha}\ \to\ \ F(x) = \frac{x^{\alpha+1}}{\alpha+1}+C$ \begin{align*} G(x) &= \frac{5 }{-5}x^{-5}-\frac{4}{-2}x^{-2}+2x+C\\ &=-x^{-5}+2x^{-2}+2x +C \end{align*} To check \begin{align*} G'(x) &=5x^{-6}-4x^{-3}+2 \\ &=\frac{5-4x^3+2x^6}{x^6}\\ &=g(x) \end{align*}
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