Integration of rational functions by partial fractions

Lessons

1. CASE 1: Denominator is a product of linear factors with no repeats.
   
   Evaluate the integral.
   1. $\int \frac{10x^2+20x-10}{x(x+2)(2x-1)}dx$
   2. $\int \frac{18}{x^3-9x}dx$
2. CASE 2: Denominator is a product of linear factors with repeats.
   
   Evaluate the integral.
   1. $\int \frac{x^2-4}{(x-1)^3}dx$
   2. $\int \frac{18x}{x^3-9x^2+15x+25}dx$
3. 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.
   1. $\int \frac{3x^2-x+9}{x^3+9x}dx$
4. CASE 4: Denominator contains irreducible quadratic factors with repeats.
   
   Evaluate $\int \frac{-3x^3+3x^2-3x+2}{x(x^2+1)^2}dx$
5. First perform long division, then partial fraction decomposition
   
   Evaluate the integral.
   1. $\int \frac{-3x^4+13x^3+22x^2-100x-10}{x^3-3x^2-10x}dx$