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RedAssigh4[1].2 - Unit Techniques of Integration Module...

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Unit: Techniques of Integration Module: Integration by Partial Fractions with Repeated Factors Distinct and Repeated Quadratic Factors www.thinkwell.com [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 1552 –rev 06/14/2001 When decomposing an expression with repeated factors, each power of the repeated factor gets its own unknown. If the factor of an expression is an irreducible quadratic, then the factor gets two unknowns when it is decomposed, one multiplied by x and the other a constant. These factors use the form Cx + D in their numerators. When the factors of the denominator in an expression you want to decompose are repeated, you have to modify the partial fraction technique. Notice here that the first factor is squared and the second is cubed. These factors are repeated. To decompose the expression, each power of the repeated factor gets its own unknown. Since the second factor was repeated three times, it gets three different fractions in the decomposition. Solving the partial fraction decomposition is

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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.

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RedAssigh4[1].2 - Unit Techniques of Integration Module...

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