What is the integral of (x-13)/(x^2-x-6) ?

The integral of (x-13)/(x^2-x-6) is 3ln|x+2|-2ln|x-3|+C

Popular >

integral of (x-13)/(x^2-x-6)

\int \frac{x - 13}{x ^{2} - x - 6} d x

3 ln ∣ x + 2 ∣ - 2 ln ∣ x - 3 ∣ + C

Solution steps

\int \frac{x - 13}{x ^{2} - x - 6} d x

Take the partial fraction of

\frac{x - 13}{x ^{2} - x - 6} : \frac{3}{x + 2} - \frac{2}{x - 3}

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

\int \frac{3}{x + 2} d x = 3 ln ∣ x + 2 ∣

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

= 3 ln ∣ x + 2 ∣ - 2 ln ∣ x - 3 ∣

Add a constant to the solution

= 3 ln ∣ x + 2 ∣ - 2 ln ∣ x - 3 ∣ + C

\int co tan^{4} (6 t) sec (6 t) d t

\int cos^{2} (nπ x) d x

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

\int \frac{1}{( x ^{2} + 1 ) ( x ^{2} + 3 )} d x

\int \frac{4 x ^{3}}{x ^{2} - 9} d x

What is the integral of (x-13)/(x^2-x-6) ?
The integral of (x-13)/(x^2-x-6) is 3ln|x+2|-2ln|x-3|+C