Explanation Given: The integral is ∫ d x 1 + x ; x = ( u 2 − 1 ) 2 . Calculation: Compute the integral by using substitution method. Let x = ( u 2 − 1 ) 2 . Then d x = 2 ( u 2 − 1 ) ⋅ 2 u d u That is, d x = 4 u ( u 2 − 1 ) d u . ∫ d x 1 + x = ∫ 4 u ( u 2 − 1 ) 1 + ( u 2 − 1 ) 2 d u = ∫ 4 u ( u 2 − 1 ) 1 + u 2 − 1 d u = ∫ 4 u ( u 2 − 1 ) u d u = 4 ∫ ( u 2 − 1 ) d u On further simplification and obtain the value of integral

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 7.5, Problem 81E

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To evaluate: The integral ∫dx1+x.

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Chapter 7.5, Problem 80E

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Chapter 7 Solutions

Calculus: Early Transcendentals (2nd Edition)

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The integral ∫ d x 1 + x .

Solution Summary: The author evaluates the value of the integral by using the substitution method.

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To evaluate: The integral ∫dx1+x.

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