Explanation Given Information: The provided indefinite integral is ∫ x x − 1 d x . Formula used: The integration by parts ∫ u d v = u v − ∫ v d u . Where, u and v are function of x . ∫ ( a x + b ) n d x = 1 a ( a x + b ) n + 1 n + 1 , n ≠ − 1 Calculation: Consider the indefinite integral ∫ x x − 1 d x Here, d v = ( x − 1 ) − 1 2 d x and u = x First find v , d v = ( x − 1 ) − 1 2 d x ∫ d v = ∫ ( x − 1 ) − 1 2 d x On further solving, v = ( x − 1 ) 1 2 ( 1 2 ) = 2 x − 1 …...…... (1) Now find d u , u = x Differentiate both side with respect x , d u d x = d ( x ) d x d u d x = 1 And, d u = 1 ⋅ d x …...…..

Calculus: An Applied Approach (Providence College: MTH 109)

9th Edition

ISBN: 9781285142616

Author: Ron Larson

Publisher: CENGAGE C

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Chapter 6.1, Problem 35E

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Chapter 6.1, Problem 34E

Chapter 6.1, Problem 36E

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Chapter 6 Solutions

Calculus: An Applied Approach (Providence College: MTH 109)

Ch. 6.1 - Prob. 1CP Ch. 6.1 - Prob. 2CP Ch. 6.1 - Prob. 3CP Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 7CP Ch. 6.1 - Prob. 1SWU Ch. 6.1 - Prob. 2SWU Ch. 6.1 - Prob. 3SWU

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The value of indefinite integral ∫ x x − 1 d x .

Solution Summary: The author explains the formula used to calculate the value of the indefinite integral displaystyle

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To calculate: The value of indefinite integral ∫xx−1dx.

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Chapter 6 Solutions