# PP 8.4 - Integration by Partial Fractions This method is...

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Integration by Partial Fractions

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This method is used to integrate rational expressions. ) ( deg ) ( deg with s polynomial ) ( ), ( , ) ( ) ( ) ( x q x p x q x p x q x p x r < = If the degree of the numerator is greater than or equal the degree of the denominator, DIVIDE first. Before you start, factor the denominator completely. That means that only linear and irreducible quadratic factors are present.
Factor in Denominator Term(s) in Decomposition n b ax ) ( + n n b ax A b ax A b ax A ) ( ... ) ( 2 2 1 + + + + + + n c bx ax ) ( 2 + + n n n c bx ax B x A c bx ax B x A c bx ax B x A ) ( ... ) ( 2 2 2 2 2 2 1 1 + + + + + + + + + + + + Factor in Denominator Term(s) in Decomposition

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Examples Find the partial fraction decomposition of each rational expression. 2 5 . 1 2 2 - + + x x x x The degree of the numerator is greater than or equal to the degree of the denominator, so we need to divide first. 2 2 4 1 2 5 2 2 2 - + + + = - + + x x x x x x x Now we need to factor the denominator completely.
) 2 )( 1 ( 2 4 1 2 2 4 1 2 5 2 2 2 + - + + = - + + + = - + + x x x x x x x x x x We need to find the partial fraction decomposition of the

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## This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.

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PP 8.4 - Integration by Partial Fractions This method is...

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