Explanation Given Information: The function is ∫ cot x d x = ln | sin x | + C . Formula Used: The rule for converting cot x in the form of sine and cosine function is cos x sin x . The following integration formula is used: ∫ 1 x d x = ln | x | + C The derivation formula, d d x sin x = cos x , where a is all-natural numbers. Proof: Consider the left side function of the provided equation ∫ cot x d x . Represent the function in the form of sine and cosine function. ∫ cot x d x = ∫ cos x sin x d x Replace the parenthetical expression with variable u . u = sin x Determine the derivative of u with respect to x. d u d x = d d x ( sin x ) = cos x Determine the value of d x . d x = 1 cos x d u Substitute the value of d x = 1 cos x d u and u = sin x into the integral ∫ cos x sin x d x

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 9.3, Problem 31E

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To prove: The derivation of the function ∫cotx dx=ln|sinx|+C where a, b are constants with a≠0.

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Chapter 9.3, Problem 30E

Chapter 9.3, Problem 32E

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Chapter 9 Solutions

Applied Calculus

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To prove: The derivation of the function ∫ cot x d x = ln | sin x | + C where a, b are constants with a ≠ 0 .

Solution Summary: The author explains the derivation of mathrmcotx in the form of sine and cosine function.

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To prove: The derivation of the function ∫cotx dx=ln|sinx|+C where a, b are constants with a≠0.

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Chapter 9 Solutions