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**Unformatted text preview: **MATH 42 — Integration by Partial Fractions — Case 4 We won’t have time to look at Case 4 in detail in class. Here is a brief sketch of the ideas involved and one concrete example illustrating their use. First, Case 4 deals with denominators involving linear expressions that may or may not repeat, as well as irreducible quadratics that may or may not repeat. The General Principle for dealing with such expressions is the following. • If the denominator contains a factor ( x- A ) then do as in Case 1. • If the denominator contains a factor ( x- A ) m with m ≥ 2 then do as in Case 2. • If the denominator contains an irreducible factor x 2 + Bx + C then do as in Case 3. • If the denominator contains an irreducible factor ( x 2 + Bx + C ) m with m ≥ 2 then use the expression D 11 x + D 10 x 2 + Bx + C + D 21 x + D 20 ( x 2 + Bx + C ) 2 + ··· + D m 1 x + D m ( x 2 + Bx + C ) m ....

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