Techniques of Integration · Partial Fractions
Partial Fractions: Distinct Linear
Decompose a rational function with distinct linear factors in the denominator into simpler fractions that can be integrated individually.
Conditions. Degree of P(x) must be less than the degree of the denominator.
- 0 variables
- 2 worked examples
- 16 in Techniques of Integration
Worked examples
Find ∫ 1/((x-1)(x+2)) dx.
- 1/((x-1)(x+2)) = A/(x-1) + B/(x+2)
- Multiply through: 1 = A(x+2) + B(x-1)
- x = 1: 1 = 3A → A = 1/3. x = -2: 1 = -3B → B = -1/3
- ∫ [(1/3)/(x-1) - (1/3)/(x+2)] dx = (1/3)ln|x-1| - (1/3)ln|x+2| + C
Answer: (1/3)ln|(x-1)/(x+2)| + C
1 more worked examplePremium
Find ∫ (5x - 4)/((x - 2)(x + 1)) dx.
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Practice
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