Explanation Given: ∫ d x cos 4 x Key Concept and Formula Used: The concept of substitution is used and the formula used : • ∫ x n = x n + 1 n + 1 + C • sec x = 1 cos x • 1 + tan 2 x = sec 2 x • d d x tan x = sec 2 x Calculation: ∫ d x cos 4 x = ∫ sec 4 x d x ( using sec x = 1 cos x ) = ∫ sec 2 x ⋅ sec 2 x d x = ∫ ( 1 + tan 2 x ) sec 2 x d x ........ (i) ( using 1 + tan 2 x = sec 2 x ) Let tan x = t Differentiate both side w...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 8, Problem 19CRE

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$\int \frac{d x}{\cos^{4} x}$

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Chapter 8, Problem 18CRE

Chapter 8, Problem 20CRE

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Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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∫ d x cos 4 x

Solution Summary: The author explains the concept of substitution and the formula used.

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∫dxcos4x

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Chapter 8 Solutions

$\int \frac{d x}{\cos^{4} x}$