Explanation Given information: ∫ ln x 2 d x Formula used: 1) Integration by parts: ∫ f ( x ) g ( x ) d x = f ( x ) G ( x ) − ∫ f ′ ( x ) G ( x ) d x Where, f ' ( x ) is derivative of f ( x ) and G ( x ) is an antiderivative of g ( x ) . 2) ln x n = n ln x Calculation: The given integral can be written as ∫ 1 ⋅ ln x 2 d x Consider, f ( x ) = ln x 2 ⇒ f ′ ( x ) = 2 x g ( x ) = 1 , G ( x ) = ∫ 1 d x = x By using the integration by part rule, ∫ 1 ⋅ ln x 2 d x = ( ln x 2 ) ⋅ x − ∫ x ⋅ 2 x d x = x ⋅ 2 ⋅ ln x − ∫ 2 d

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 9, Problem 13RE

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To calculate: The value of indefinite integral ∫lnx2dx.

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Chapter 9, Problem 12RE

Chapter 9, Problem 14RE

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The value of indefinite integral ∫ ln x 2 d x .

Solution Summary: The author explains how to calculate the value of an indefinite integral, using the integration by part rule.

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To calculate: The value of indefinite integral ∫lnx2dx.

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Chapter 9 Solutions