Explanation Given information: The indefinite integral, ∫ tan 2 x sec 3 x d x Concept used: Reduction formula: ∫ sec n ( x ) d x = n − 2 n − 1 ∫ sec n − 2 ( x ) d x + sec n − 2 ( x ) tan ( x ) n − 1 ∫ sec x d x = ln ( sec x + tan x ) Calculation: To evaluate the indefinite integral, first we rewrite the integrand using the Pythagorean identity. So we get ∫ tan 2 x sec 3 x d x = ∫ ( sec 2 x − 1 ) sec 3 x d x = ∫ ( sec 5 x − sec 3 x ) d x = ∫ sec 5 x d x − ∫ sec 3 x d x Now we use the reduction formula. So to solve the first integral, using n = 5 , we get ∫ tan 2 x sec 3 x d x = ∫ sec 5 x d x − ∫ sec 3 x d x = 3 4 ∫ sec 3 ( x ) d x + sec 3 ( x ) tan ( x ) 4 − ∫ sec 3 x d x = sec 3 ( x ) tan ( x ) 4 − 1 4 ∫ sec 3 x d x

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Chapter 7.2, Problem 36E

To determine

To evaluate the integral ∫tan2xsec3x dx

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Chapter 7.2, Problem 35E

Chapter 7.2, Problem 37E

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Chapter 7 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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To evaluate the integral ∫ tan 2 x sec 3 x d x

Solution Summary: The author explains how to evaluate the indefinite integral using the Pythagorean identity.

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To evaluate the integral ∫tan2xsec3x dx

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Chapter 7 Solutions