Explanation Formula used: ∫ x n d x = x n + 1 n + 1 + C (1) Calculation: The given integral is ∫ e x 2 e x − 1 d x . Use formula (1) and obtain the indefinite integral ∫ e x 2 e x − 1 d x . Apply substitution as, u = 2 e x − 1 . Differentiate u = 2 e x − 1 with respect to x. Then, d u d x = 2 e x d u = 2 e x d x Substitute u = 2 e x − 1 and d u = 2 e x d x in ∫ e x 2 e x − 1 d x , ∫ e x 2 e x − 1 d x = ∫ 1 2 u d u = 1 2 ∫ 1 u d u = 1 2 ln u + C Since u = 2 e x − 1 , the above integral becomes ∫ e x 2 e x − 1 d x = 1 2 ln ( 2 e x − 1 ) + C

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134674148

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

Publisher: PEARSON

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Chapter 12.2, Problem 68E

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To find: The indefinite integral of ∫ex2ex−1dx and check the result by differentiation.

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Chapter 12.2, Problem 67E

Chapter 12.2, Problem 69E

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Chapter 12 Solutions

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 12.1 - Matched Problem 1 Note that Find all...Ch. 12.1 - Prob. 2MP Ch. 12.1 - Prob. 3MP Ch. 12.1 - Prob. 4MP Ch. 12.1 - Prob. 5MP Ch. 12.1 - Prob. 6MP Ch. 12.1 - Prob. 1ED Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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The indefinite integral of ∫ e x 2 e x − 1 d x and check the result by differentiation.

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To find: The indefinite integral of ∫ex2ex−1dx and check the result by differentiation.

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Chapter 12 Solutions