# Integration Of Rational Functions (1) - Integration Of...

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1 Integration Of Rational Functions By Partial Fractions Polynomial Factorization Theorem : The factorization of any polynomial Q ( x ) with real coefficients is the product of polynomials of the form ( ax + b ) i and ( ax 2 + bx + c ) j where i and j are nonnegative integer and ax 2 + bx + c is irreducible over the real numbers.
2 Suppose that is a rational expression with the degree of P ( x ) is less than the degree of Q ( x ) , and the polynomials P ( x ) and Q ( x ) have real coefficients. If the rational expression is in lowest terms, then it can be written as a sum of partial fractions = F 1 + F 2 + … + F r where each term F i ( i = 1,2, … , r ) has one of the ) ( ) ( x Q x P ) ( ) ( x Q x P ) ( ) ( x Q x P forms: where ax 2 + bx + c is irreducible over the real numbers. m n c bx ax C Bx b ax A ) ( or ) ( 2 + + +
3 To write in this way, we completely factor
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