Explanation Given: ∫ x ( 3 + 2 x ) 2 d x Formula used: The integration rule: ∫ [ f ( u ) ± g ( u ) ] d u = ∫ f ( u ) d u ± ∫ g ( u ) d u . ∫ x n d x = x n + 1 n + 1 + c . ∫ 1 x d x = ln | x | + c Calculation: Consider the integral: ∫ x ( 3 + 2 x ) 2 d x Now, ∫ x ( 3 + 2 x ) 2 d x = ∫ x [ 3 2 + ( 2 x ) 2 + 2 × 3 × 2 x ] d x = ∫ x [ 9 + 4 x 2 + 12 x ] d x = ∫ ( 9 x + 4 x + 12 ) d x Apply integration rule: ∫ [ f ( u ) ± g ( u ) ] d u = ∫ f ( u ) d u ±

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ISBN: 9781285057095

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 8.1, Problem 28E

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To calculate: The indefinite integral ∫x(3+2x)2dx by using integration formula.

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Chapter 8.1, Problem 27E

Chapter 8.1, Problem 29E

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The indefinite integral ∫ x ( 3 + 2 x ) 2 d x by using integration formula.

Solution Summary: The author explains how to calculate the indefinite integral 'displaystyle int xleft' using the integration formula.

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To calculate: The indefinite integral ∫x(3+2x)2dx by using integration formula.

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Chapter 8 Solutions