Explanation Given information: The integral ∫ sec 2 ( 2 x + 1 ) d x . Explanation: The chain rule of thederivative of d d x ( tan g ( x ) ) is d d x ( tan g ( x ) ) = [ sec 2 g ( x ) ] × g ' ( x ) By dividing g ' ( x ) on both sides, ⇒ d d x ( tan g ( x ) ) g ' ( x ) = sec 2 g ( x ) If g ' ( x ) is constant, then by integration on both sides, ⇒ ∫ sec 2 g ( x ) d x = tan g ( x ) g ' ( x ) + C Now, in integral ∫ sec 2 ( 2 x + 1 ) d x , g ( x ) = 2 x + 1 . By taking derivative of g ( x ) = 2 x + 1 ⇒ g ' ( x ) = 2 Since g ' ( x ) is constant, by applying theabove formula ∫ sec 2 g ( x ) d x = tan g ( x ) g ' ( x ) + C

15th Edition

ISBN: 9780137590896

Author: Larry J. Goldstein; David C. Lay; David I. Schneider; Nakhle H. Asmar; William Edward Tavernetti

Publisher: Pearson Education (US)

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Chapter 8.4, Problem 36E

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The integration ∫sec2 (2x + 1) dx.

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Chapter 8.4, Problem 35E

Chapter 8.4, Problem 37E

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The integration ∫ sec 2 ( 2 x + 1 ) d x .

Solution Summary: The author explains the chain rule of the derivative of dx(mathrmtang

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The integration ∫sec2 (2x + 1) dx.

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