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: 12

Answer

$\frac{3}{5}x^{5/3}+\frac{2}{5}x^{5/2}+C$

Work Step by Step

Start with original function: $\int (\sqrt[3] {x^{2}} + x\sqrt x)dx$. Rewrite radicals as fractional powers: $\int (x^{2/3}+x^{3/2})dx$. Use power rule for antiderivatives to integrate each term: $\frac{x^{5/3}}{\frac{5}{3}}+\frac{x^{5/2}}{\frac{5}{2}}+C$. Simplify fractions to arrive at answer: $\frac{3}{5}x^{5/3}+\frac{2}{5}x^{5/2}+C$.
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