What is the integral of (x-3)/(x^2-5x+6) ?

The integral of (x-3)/(x^2-5x+6) is ln|x-2|+C

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integral of (x-3)/(x^2-5x+6)

\int \frac{x - 3}{x ^{2} - 5 x + 6} d x

ln ∣ x - 2 ∣ + C

Solution steps

\int \frac{x - 3}{x ^{2} - 5 x + 6} d x

Apply u-substitution

= \int \frac{1}{u + 1} d u

Apply u-substitution

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln ∣ x - 3 + 1 ∣

Simplify

= ln ∣ x - 2 ∣

Add a constant to the solution

= ln ∣ x - 2 ∣ + C

What is the integral of (x-3)/(x^2-5x+6) ?
The integral of (x-3)/(x^2-5x+6) is ln|x-2|+C