Explanation Formula used: ∫ x n d x = x n + 1 n + 1 + C (1) Calculation: The given integral is ∫ x 2 ( x 3 + 2 ) 2 d x . Use formula (1) and obtain the indefinite integral ∫ x 2 ( x 3 + 2 ) 2 d x . Apply substitution as, u = x 3 + 2 . Differentiate u = x 3 + 2 with respect to x. d u d x = 3 x 2 d u = 3 x 2 d x 1 3 d u = x 2 d x Substitute u = x 3 + 2 and 1 3 d u = x 2 d x in ∫ x 2 ( x 3 + 2 ) 2 d x , ∫ x 2 ( x 3 + 2 ) 2 d x = ∫ u 2 3 d u = 1 3 ∫ u 2 d u = 1 3 u 2 + 1 2 + 1 + C = 1 9 u 3 + C Since u = x 3 + 2 , the above integral becomes ∫ x 2 ( x 3 + 2 ) 2 d x = 1 9 ( x 3 + 2 ) 3 + C

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321869838

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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Chapter 5.2, Problem 63E

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To find: The value of the indefinite integral $∫x2(x3+2)2dx$ and check the obtained value by differentiation.

z

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Chapter 5.2, Problem 62E

Chapter 5.2, Problem 64E

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Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

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The value of the indefinite integral ∫ x 2 ( x 3 + 2 ) 2 d x and check the obtained value by differentiation. z

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