What is the integral of (x^2-8x+15)/(x^2-6x+5) ?

The integral of (x^2-8x+15)/(x^2-6x+5) is -2ln|x-1|+x+C

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integral of (x^2-8x+15)/(x^2-6x+5)

\int \frac{x ^{2} - 8 x + 15}{x ^{2} - 6 x + 5} d x

- 2 ln ∣ x - 1 ∣ + x + C

Solution steps

\int \frac{x ^{2} - 8 x + 15}{x ^{2} - 6 x + 5} d x

\frac{x ^{2} - 8 x + 15}{x ^{2} - 6 x + 5} = - \frac{2}{x - 1} + 1

= \int - \frac{2}{x - 1} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{2}{x - 1} d x + \int 1 d x

\int \frac{2}{x - 1} d x = 2 ln ∣ x - 1 ∣

\int 1 d x = x

= - 2 ln ∣ x - 1 ∣ + x

Add a constant to the solution

= - 2 ln ∣ x - 1 ∣ + x + C

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What is the integral of (x^2-8x+15)/(x^2-6x+5) ?
The integral of (x^2-8x+15)/(x^2-6x+5) is -2ln|x-1|+x+C