What is the integral of (x+4)/((x+1)(x-2)) ?

The integral of (x+4)/((x+1)(x-2)) is -ln|x+1|+2ln|x-2|+C

Popular >

integral of (x+4)/((x+1)(x-2))

\int \frac{x + 4}{( x + 1 ) ( x - 2 )} d x

- ln ∣ x + 1 ∣ + 2 ln ∣ x - 2 ∣ + C

Solution steps

\int \frac{x + 4}{( x + 1 ) ( x - 2 )} d x

Take the partial fraction of

\frac{x + 4}{( x + 1 ) ( x - 2 )} : - \frac{1}{x + 1} + \frac{2}{x - 2}

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

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

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

= - ln ∣ x + 1 ∣ + 2 ln ∣ x - 2 ∣

Add a constant to the solution

= - ln ∣ x + 1 ∣ + 2 ln ∣ x - 2 ∣ + C

\int e^{- e^{- x}} d e^{- e^{- x}}

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

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

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

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

What is the integral of (x+4)/((x+1)(x-2)) ?
The integral of (x+4)/((x+1)(x-2)) is -ln|x+1|+2ln|x-2|+C