Explanation Given: The integral is: ∫ x ( x 2 − 6 x + 10 ) 2 d x . Formula used: Use the formula 1, 23, and 25 from the table of integrals: ∫ u n d u = u n + 1 n + 1 + C ∫ 1 a 2 + u 2 d u = 1 a arctan u a + C ∫ 1 ( a 2 + u 2 ) n d u = 1 2 a 2 ( n − 1 ) [ u ( a 2 + u 2 ) n − 1 + ( 2 n − 3 ) ∫ 1 ( a 2 + u 2 ) n − 1 d u ] + C Calculation: Consider the provided integral, ∫ x ( x 2 − 6 x + 10 ) 2 d x = 1 2 ∫ 2 x + 6 − 6 ( x 2 − 6 x + 10 ) 2 d x = 1 2 ∫ 2 x + 6 ( x 2 − 6 x + 10 ) 2 d x − 3 ∫ 1 ( ( x − 3 ) 2 + 1 ) 2 d x Now, use the formula 1 to solve first integral and formula 25 to solve the second integral: For integral 1, let u = x 2 − 6 x + 10 . Then, d u = ( 2 x − 6 ) d x . And for integral 2, let a = 1 , n = 2 and u = x + 3 . Then, d u = d x . Therefore, ∫ x ( x 2 − 6 x + 10 ) 2 d x = 1 2 ∫ ( x 2 − 6 x + 10 ) − 2 ( 2 x − 6 ) d x + 3 ∫ 1 ( ( x − 3 ) 2 + 1 ) 2 d x = [ 1 2 ( ( x 2 − 6 x + 10 ) − 2 + 1 −</

Calculus Of A Single Variable With Calcchat And Calcview, 11e

11th Edition

ISBN: 9781337275583

Author: Larson

Publisher: Cengage Learning

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Chapter 8.7, Problem 35E

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To calculate: The value of the indefinite integral ∫x(x2−6x+10)2dx by the use of a table of integrals.

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Chapter 8.7, Problem 34E

Chapter 8.7, Problem 36E

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Calculus Of A Single Variable With Calcchat And Calcview, 11e

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The value of the indefinite integral ∫ x ( x 2 − 6 x + 10 ) 2 d x by the use of a table of integrals.

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To calculate: The value of the indefinite integral ∫x(x2−6x+10)2dx by the use of a table of integrals.

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Chapter 8 Solutions