Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 4 - Applications of the Derivative - 4.9 Antiderivatives - 4.9 Exercises: 30

Answer

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

Work Step by Step

$$\eqalign{ & \int {6\root 3 \of x } dx \cr & = 6\int {\root 3 \of x } dx \cr & = 6\int {{x^{1/3}}} dx \cr & {\text{use power rule for indefinite integrals}} \cr & = 6\left( {\frac{{{x^{4/3}}}}{{4/3}}} \right) + C \cr & {\text{simplify}} \cr & = \frac{9}{2}{x^{4/3}} + C \cr & {\text{check by differentiation}} \cr & {\text{ = }}\frac{d}{{dx}}\left( {\frac{9}{2}{x^{4/3}} + C} \right) \cr & = \frac{9}{2}\left( {\frac{4}{3}} \right){x^{1/3}} + C \cr & = 6{x^{1/3}} + C \cr & = 6\root 3 \of x + C \cr} $$
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