Explanation Given: The integral ∫ x 2 + 2 x x 3 − x 2 + x − 1 d x Formula Used: In partial fraction, for integral of type ∫ x 2 + a ( x + b ) ( x + c ) d x , it can be simplified as x 2 + a ( x + b ) ( x 2 + c ) = A ( x + b ) + B x + C ( x 2 + c ) Calculation: Here the integral is ∫ x 2 + 2 x x 3 − x 2 + x − 1 d x . Here the equation x 3 − x 2 + x − 1 can be simplified as, x 3 − x 2 + x − 1 = ( x 2 ) ( x − 1 ) + 1 ( x − 1 ) = ( x − 1 ) ( x 2 + 1 ) Thus, ∫ x 2 + 2 x x 3 − x 2 + x − 1 d x can be written as x 2 + 2 x x 3 − x 2 + x − 1 = A x − 1 + B x + C x 2 + 1 x 2 + 2 x ( x − 1 ) ( x 2 + 1 ) = A ( x 2 + 1 ) + ( B x + C ) ( x<

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ISBN: 9781337888950

Author: Larson

Publisher: CENGAGE L

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Chapter 8, Problem 39RE

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To calculate: The integral ∫x2+2xx3−x2+x−1dx using partial fractions.

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Chapter 8, Problem 38RE

Chapter 8, Problem 40RE

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The integral ∫ x 2 + 2 x x 3 − x 2 + x − 1 d x using partial fractions.

Solution Summary: The author explains how to calculate the integral displaystyle 'int' using partial tions.

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Chapter 8 Solutions