Explanation Given information: ∫ x 3 d x x 2 − 2 x + 1 Formula: x 2 − 2 x + 1 = ( x − 1 ) 2 ∫ d x x = [ ln | x | ] + C ∫ x n d x = [ x n + 1 n + 1 ] + C Calculation: Express the integral through long division as below eliminating the cubic term. ∫ x 3 d x x 2 − 2 x + 1 = ∫ ( x + 2 x 2 − x x 2 − 2 x + 1 ) d x Express the integral through long division as below eliminating the square term. ∫ x 3 d x x 2 − 2 x + 1 = ∫ ( x + 2 + 3 x − 2 x 2 − 2 x + 1 ) d x ∫ x 3 d x x 2 − 2 x + 1 = ∫ ( x + 2 ) d x + ∫ 3 x − 2 ( x − 1 ) 2 d x (1) Express the integrand as a sum of partial fractions with undetermined coefficients. 3 x − 2 ( x − 1 ) 2 = A x − 1 + B ( x − 1 ) 2 (2) Simplify the above equation as below

Thomas' Calculus - MyMathLab Integrated Review

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ISBN: 9780134786223

Author: Hass

Publisher: PEARSON

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Chapter 8, Problem 98PE

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Chapter 8, Problem 97PE

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