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: 11

Answer

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

Work Step by Step

Start with function: $\int (3\sqrt x-2\sqrt[3] x)dx$ Rewrite square root and third root in fractional power form: $\int (3x^{1/2}-2x^{1/3})dx$. Use power rule for antiderivatives to integrate both terms: $\frac{3x^{3/2}}{\frac{3}{2}}-\frac{2x^{4/3}}{\frac{4}{3}}+C$. Simplify fractions to arrive at answer: $2x^{3/2}-\frac{3}{2}x^{4/3}+C$.
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