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

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

Popular >

integral of (x-6)/(x^2-2x)

\int \frac{x - 6}{x ^{2} - 2 x} d x

3 ln ∣ x ∣ - 2 ln ∣ x - 2 ∣ + C

Solution steps

\int \frac{x - 6}{x ^{2} - 2 x} d x

Take the partial fraction of

\frac{x - 6}{x ^{2} - 2 x} : \frac{3}{x} - \frac{2}{x - 2}

= \int \frac{3}{x} - \frac{2}{x - 2} 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{3}{x} d x - \int \frac{2}{x - 2} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 3 ln ∣ x ∣ - 2 ln ∣ x - 2 ∣

Add a constant to the solution

= 3 ln ∣ x ∣ - 2 ln ∣ x - 2 ∣ + C

\int \frac{1}{x ( 1 - 1 - x )} d x

\int \frac{- 9 x ^{2}}{4} d x

\int \frac{8 - 3 x}{( x + 1 ) ( x ^{2} - 4 x + 6 )} d x

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

\int 2 cos^{3} (x) sin (x) d x

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