Explanation The given integral is ∫ 1 x 2 1 + x d x . Consider u = 1 + x and calculate the value of d u . u = 1 + x d u = 1 2 1 + x d x 2 1 + x d u = d x Substitute u = 1 + x and 2 1 + x d u = d x in the integral ∫ 1 x 2 1 + x d x , ∫ 1 x 2 1 + x d x = ∫ 2 ( u 2 − 1 ) 2 d u = 2 ∫ 1 ( u 2 − 1 ) 2 d u = 2 ∫ 1 u 4 − 2 u 2 + 1 d u = 2 ∫ 1 ( u + 1 ) 2 ( u − 1 ) 2 d u Simplify further, ∫ 1 x 2 1 + x d x = 2 ∫ 1 4 ( u + 1 ) + 1 4 ( u + 1 ) 2 − 1 4 ( u − 1 ) + 1 4 ( u − 1 ) 2 d u = 2 ( ∫ 1 4 ( u + 1 ) d u + ∫ 1 4 ( u + 1 ) 2 d u − ∫ 1 4 ( u − 1 ) d u + ∫ 1 4 ( u − 1 ) 2 d u ) = 2 ( 1 4 ln | u + 1 | − 1 4 ( u + 1 ) − 1 4 ln | u − 1 | − 1 4 ( u − 1 ) ) = 2 ( 1 4 ln | 1 + x + 1 | − 1

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321869838

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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Chapter 6, Problem 10RE

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Chapter 6, Problem 9RE

Chapter 6, Problem 11RE

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Chapter 6 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

Ch. 6.1 - Matched Problem 1 Find the area bounded by f(x) =...Ch. 6.1 - Matched Problem 2 Find the area between the graph...Ch. 6.1 - Prob. 3MP Ch. 6.1 - Matched Problem 4Find the area bounded by f(x) =6 ...Ch. 6.1 - Matched Problem 5Find the area bounded by f(x)=2x2...Ch. 6.1 - Matched Problem 6Find the area (to three decimal...Ch. 6.1 - Prob. 7MP Ch. 6.1 - Prob. 1ED Ch. 6.1 - In Problems 18, use geometric formulas to find the...Ch. 6.1 - In Problems 18, use geometric formulas to find the...

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The value of the integral ∫ 1 x 2 1 + x d x .

Solution Summary: The author calculates the value of the integral displaystyle 'int' -12mathrmlnleft

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Chapter 6 Solutions