# Integration of rational functions by partial fractions

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##### Examples

###### Lessons

**CASE 1: Denominator is a product of linear factors with no repeats.**

Evaluate the integral.**CASE 2: Denominator is a product of linear factors with repeats.**

Evaluate the integral.**CASE 3: Denominator contains irreducible quadratic factors with no repeats.**

*** recall: $\int \frac{dx}{x^2+a^2}=\frac{1}{a}tan^{-1}(\frac{x}{a})+C$ ***

Evaluate the integral.**CASE 4: Denominator contains irreducible quadratic factors with repeats.**

Evaluate $\int \frac{-3x^3+3x^2-3x+2}{x(x^2+1)^2}dx$**First perform long division, then partial fraction decomposition**

Evaluate the integral.