Integrate f(x): f(x) = (3x +2) / (x^2 - 5x +6)
Split into partial fractions: (3x +2) / (x2 - 5x +6) = A / (x-3) + B / (x-2) => 3x + 2 = A(x-2) + B(x-3) let x = 2: 8 = -B => B = -8 let x = 3: 11 = A => A = 11 Now we can integrate f(x) = 11 / (x-3) - 8 / (x-2): Giving: 11 ln(x-3) - 8 ln(x-2) + C
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