Explanation Given: The integral is: ∫ 0 5 x 2 ( 5 + 2 x ) 2 d x . Formula used: Use the formula 7 from the table of integrals: ∫ u 2 ( a + b u ) 2 d u = 1 b 3 ( b u − a 2 a + b u − 2 a ln | a + b u | ) + C Calculation: Consider the provided integral, ∫ 0 5 x 2 ( 5 + 2 x ) 2 d x Now, use the formula 7 to solve the integral. Let b = 2 and u = x . Then d u = d x . ∫ x 2 ( 5 + 2 x ) 2 d x = 1 2 3 ( 2 x − 5 2 5 + 2 x − 2 ⋅ 5 ln | 5 + 2 x | ) + C

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Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 8.6, Problem 44E

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To calculate: The value of the definite integral ∫05x2(5+2x)2dx by the use of a table of integrals.

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Chapter 8.6, Problem 43E

Chapter 8.6, Problem 45E

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The value of the definite integral ∫ 0 5 x 2 ( 5 + 2 x ) 2 d x by the use of a table of integrals.

Solution Summary: The author explains how to calculate the value of the definite integral, using the formula 7 from the table of integrals.

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To calculate: The value of the definite integral ∫05x2(5+2x)2dx by the use of a table of integrals.

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Chapter 8 Solutions