Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 238: 24

Answer

$\dfrac{x}{5}+\dfrac{1}{x^2}+x^2+C$

Work Step by Step

Since, we have $\int (\dfrac{1}{5}-\dfrac{2}{x^3}+2x) dx=\dfrac{x}{5}+\dfrac{1}{x^2}+x^2+C$ Also, $\dfrac{d}{dx}(\dfrac{x}{5}+\dfrac{1}{x^2}+x^2+C)=\dfrac{1}{5}-\dfrac{2}{x^3}+2x$ Thus, the derivative of the integral is integrand. So, the answer is correct.
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