Question

∫(x^2-5x+9)/(x^2-5x+6)

Answer 1

$$\frac{x^2-5x+9}{x^2-5x+6}=\frac{x^2-5x+6+3}{x^2-5x+6}=1+\frac3{x^2-5x+6}$$

Answer 2

notice we can factor our denominator \(x^2-5x+6=(x-3)(x-2)\) now use the method of partial fractions to split \(\dfrac3{(x-2)(x-3)}\) into 'simpler' rational functions we can integrate