Explanation Given: The integral function is ∫ x 2 − 6 x + 2 x 3 + 2 x 2 + x d x . Formula used: ∫ 1 x d x = ln | x | + C . Calculation: Consider the following indefinite integral, ∫ x 2 − 6 x + 2 x 3 + 2 x 2 + x d x The above integral function can be written as, x 2 − 6 x + 2 x 3 + 2 x 2 + x = x 2 − 6 x + 2 x ( x 2 + 2 x + 1 ) = x 2 − 6 x + 2 x ( x + 1 ) 2 Now by using partial fraction method we get, x 2 − 6 x + 2 x ( x + 1 ) 2 = A x + B x + 1 + C ( x + 1 ) 2 x 2 − 6 x + 2 = A ( x + 1 ) 2 + B x ( x + 1 ) + C x By simplifying further we get, At x = 0 , ( 0 ) 2 − 6 ( 0 ) + 2 = A ( 0 + 1 ) 2 + B ( 0 ) ( ( 0 ) + 1 ) + C ( 0 ) A = 2 At x = − 1 . ( − 1 ) 2 − 6 ( − 1 ) + 2 = A ( − 1 + 1 ) 2 + B ( − 1 ) ( − 1 + 1 ) + C ( − 1 ) C = − 9 At x = 1

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ISBN: 9781337275361

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 8.5, Problem 13E

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To calculate: The indefinite integral for the given function, by using partial fractions.

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Chapter 8.5, Problem 12E

Chapter 8.5, Problem 14E

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The indefinite integral for the given function, by using partial fractions.

Solution Summary: The author calculates the indefinite integral for the given function, by using partial tions. The above integral function can be written as cx2-6x+2

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To calculate: The indefinite integral for the given function, by using partial fractions.

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