Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 4 - Section 4.9 - Antiderivatives - 4.9 Exercises - Page 355: 3


$\frac{x^{4}}{2}-\frac{2x^{3}}{9} + \frac{5x^{2}}{2}+C$

Work Step by Step

Start with function $2x^{3}-\frac{2}{3}x^2+5x$. Use power rule for antiderivatives (antiderivative of $x^{n}$ is $\frac{x^{n+1}}{n+1}$) on each of the three terms. Since the terms are added, the antiderivatives are also added. Add constant to make it most general form. We arrive at the answer $\frac{x^{4}}{2}-\frac{2x^{3}}{9} + \frac{5x^{2}}{2}+C$.
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