Explanation Formula used: The integral formula of the form is ∫ 1 a 2 + x 2 d x = 1 a tan − 1 x a + C . Calculation: The given integral is ∫ x − 2 + x − 3 x − 1 + 16 x − 3 d x . The integrand is f ( x ) = x − 2 + x − 3 x − 1 + 16 x − 3 . In order to evaluate the integral, first eliminate the negative powers of integrand. f ( x ) = ( x − 2 + x − 3 ) x 3 ( x − 1 + 16 x − 3 ) x 3 = ( x − 2 + 3 + x − 3 + 3 ) ( x − 1 + 3 + 16 x − 3 + 3 ) = x 1 + x 0 x 2 + 16 x 0 = x + 1 x 2 + 16 Split off the integral ∫ x − 2 + x − 3 x − 1 + 16 x − 3 d x as follows. ∫ x − 2 + x − 3 x − 1 + 16 x − 3 d x = ∫ x + 1 x 2 + 16 d x = ∫ x x 2 + 16 d x + ∫ 1 x 2 + 16 d x Calculate the first integral ∫ x x 2 + 16 d x by substitution method

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 8.6, Problem 14E

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To evaluate: The integral ∫x−2+x−3x−1+16x−3dx.

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Chapter 8.6, Problem 13E

Chapter 8.6, Problem 15E

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Calculus, Single Variable: Early Transcendentals (3rd Edition)

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The integral ∫ x − 2 + x − 3 x − 1 + 16 x − 3 d x .

Solution Summary: The author evaluates the integral by eliminating the negative powers of the integrand.

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To evaluate: The integral ∫x−2+x−3x−1+16x−3dx.

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