What is the integral of (x+19)/(x^2-7x-8) ?

The integral of (x+19)/(x^2-7x-8) is -2ln|x+1|+3ln|x-8|+C

Popular >

integral of (x+19)/(x^2-7x-8)

\int \frac{x + 19}{x ^{2} - 7 x - 8} d x

- 2 ln ∣ x + 1 ∣ + 3 ln ∣ x - 8 ∣ + C

Solution steps

\int \frac{x + 19}{x ^{2} - 7 x - 8} d x

Take the partial fraction of

\frac{x + 19}{x ^{2} - 7 x - 8} : - \frac{2}{x + 1} + \frac{3}{x - 8}

= \int - \frac{2}{x + 1} + \frac{3}{x - 8} 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 \frac{3}{x - 8} d x

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

\int \frac{3}{x - 8} d x = 3 ln ∣ x - 8 ∣

= - 2 ln ∣ x + 1 ∣ + 3 ln ∣ x - 8 ∣

Add a constant to the solution

= - 2 ln ∣ x + 1 ∣ + 3 ln ∣ x - 8 ∣ + C

\int e^{- x} f (e^{- x}) d x

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

\int 2 sin (x) + 4 d x

\int \frac{π}{4 W} cos (\frac{π x}{2 W}) d x

\int (2 x - 1) sin (2 x) d x

What is the integral of (x+19)/(x^2-7x-8) ?
The integral of (x+19)/(x^2-7x-8) is -2ln|x+1|+3ln|x-8|+C