Calculus: Early Transcendentals 8th Edition

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

Chapter 7 - Section 7.5 - Strategy for Integration - 7.5 Exercises - Page 508: 57


$$\int x\sqrt[3]{x+c}dx=\frac{3}{7}(x+c)^{\frac{7}{3}}-\frac{3}{4}c(x+c)^{\frac{4}{3}}+C$$

Work Step by Step

$$let\,t = \sqrt[3]{x+c},dx=3t^{2}dt$$ $$\int x\sqrt[3]{x+c}dx=3\int (t^{6}-ct^{3})dt$$ $$=\frac{3}{7}t^{7}-\frac{3}{4}ct^{4}+C$$ $$=\frac{3}{7}(x+c)^{\frac{7}{3}}-\frac{3}{4}c(x+c)^{\frac{4}{3}}+C$$
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