Partial Fractions (Distinct Linear Factors) (Calculus II)
Free printable university Calculus II worksheet: integrating rational functions by partial fraction decomposition with distinct linear factors, including the cover-up method. Decompositions are recombined and verified exactly.
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Calculus II · Math worksheet
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Math
Integration Techniques: Partial Fractions (Distinct Linear Factors)
Each integrand is a proper rational function whose denominator factors into distinct linear factors. Decompose it as a sum of terms A/(x - r), find each constant (the cover-up method is fastest), then integrate term by term to logarithms. Include + C.
- 1.Use partial fractions to evaluate the integral of (-6x - 3)/((x + 2)(x - 1)) dx.
- 2.Use partial fractions to evaluate the integral of (-32)/( + 2x - 15) dx.
- 3.Use partial fractions to evaluate the integral of (-6x + 21)/((x - 2)(x - 5)) dx.
- 4.Use partial fractions to evaluate the integral of (4x + 9)/( + 3x) dx.
- 5.Use partial fractions to evaluate the integral of (x + 11)/((x + 1)(x - 4)) dx.
- 6.Use partial fractions to evaluate the integral of (3x + 1)/( - 2x - 15) dx.
- 7.Use partial fractions to evaluate the integral of (-7x^2 - 44x - 63)/((x + 5)(x + 3)(x + 2)) dx.
- 8.Use partial fractions to evaluate the integral of (-3x^2 + 6x - 7)/((x + 1)(x - 1)(x - 3)) dx.
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