Explanation Given: ∫ d x x ( a x + b ) = 1 b ln | x a x + b | + C Calculation: The given integral can be evaluated as Consider, 1 x ( a x + b ) = A x + B a x + b → ( 1 ) ⇒ 1 = A ( a x + b ) + B x When x = 0 , 1 = b A ⇒ A = 1 b When x = 1 , 1 = A ( a + b ) + B ⇒ 1 b ( a + b ) + B = 1 ⇒ B = 1 − a b − 1 ⇒ B = − a b Therefore equation (1) becomes, 1 x ( a x + b ) = 1 b x − a b a x + b ∴ ∫ d x x ( a x + b ) = ∫ ( 1 b x − a b a x + b )

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 7.4, Problem 57PS

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To derive the formula ∫dxx( ax+b)=1bln|x ax+b|+C

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Chapter 7.4, Problem 56PS

Chapter 7.4, Problem 58PS

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Chapter 7 Solutions

Calculus

Ch. 7.1 - Prob. 1PS Ch. 7.1 - Prob. 2PS Ch. 7.1 - Prob. 3PS Ch. 7.1 - Prob. 4PS Ch. 7.1 - Prob. 5PS Ch. 7.1 - Prob. 6PS Ch. 7.1 - Prob. 7PS Ch. 7.1 - Prob. 8PS Ch. 7.1 - Prob. 9PS Ch. 7.1 - Prob. 10PS

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To derive the formula ∫ d x x ( a x + b ) = 1 b ln | x a x + b | + C

Solution Summary: The author explains how the given integral can be evaluated as l1x(ax+b)=

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To derive the formula ∫dxx( ax+b)=1bln|x ax+b|+C

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Chapter 7 Solutions