L16a - Integration by the Method of Partial Fractions _part 1_

# L16a - Integration by the Method of Partial Fractions _part 1_

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Integration By Partial Fractions (Section 7.4) Division: When the degree of the numerator is greater than or equal to the degree of the denominator, divide. Ex. x 3 x 2 6 x 2 1 dx Ex: 3 x 4 x 2 dx

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Partial Fractions Case 1: Suppose a rational expression R ( x ) Q ( x ) has a denominator that can be rewritten as a product of distinct linear factors: R ( x ) Q ( x ) R ( x ) a 1 x b 1  a 2 x b 2 ... a n x b n Then we can rewrite the expression as a sum: R ( x ) Q ( x ) A 1 a 1 x b 1 A 2 a 2 x b 2 ... A n a n x b n Ex. 2 x 6 x 2 2 x 3 dx
Ex. Find the partial fraction decomposition of x 4 x 2 2 x 8 . Ex. Find the partial fraction decomposition of 2 35 34 x xx .

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Case 2:

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L16a - Integration by the Method of Partial Fractions _part 1_

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