Explanation Given Information: The provided function is ∫ 4 x sec 2 ( 2 x 2 − 1 ) d x . Formula Used: If u is a function of x, then the rule to evaluate an integral is ∫ f d x = ∫ ( f d u / d x ) d u where d u d x a derivative of the function with respect to x and solve for d x in terms of d u . If the function is f ( x ) = sec 2 ( a x ) , then the formula for the integration of the function is given by ∫ sec 2 ( a x ) d x = 1 a tan ( a x ) + C . Calculation: Consider the function ∫ 4 x sec 2 ( 2 x 2 − 1 ) d x . Replace the parenthetical expression with variable u . u = 2 x 2 − 1 Determine the derivative of u with respect to x , d u d x = d d x ( 2 x 2 − 1 ) d u d x = 4 x Determine the value of d x , d x = 1 4 x d u Substitute the value of d x into the integral

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 9, Problem 17RE

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To calculate: The integral of the function ∫4xsec2(2x2−1)dx.

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Chapter 9, Problem 16RE

Chapter 9, Problem 18RE

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Chapter 9 Solutions

Applied Calculus

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The integral of the function ∫ 4 x sec 2 ( 2 x 2 − 1 ) d x .

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Chapter 9 Solutions