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

The integral of (x-4)/(x+2) is x+2-6ln|x+2|+C

Popular >

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

\int \frac{x - 4}{x + 2} d x

x + 2 - 6 ln ∣ x + 2 ∣ + C

Solution steps

\int \frac{x - 4}{x + 2} d x

Apply u-substitution

: \int \frac{u - 6}{u} d u

= \int \frac{u - 6}{u} d u

Expand

\frac{u - 6}{u} : 1 - \frac{6}{u}

= \int 1 - \frac{6}{u} d u

Apply the Sum Rule:

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

= \int 1 d u - \int \frac{6}{u} d u

\int 1 d u = u

\int \frac{6}{u} d u = 6 ln ∣ u ∣

= u - 6 ln ∣ u ∣

Substitute back

u = x + 2

= x + 2 - 6 ln ∣ x + 2 ∣

Add a constant to the solution

= x + 2 - 6 ln ∣ x + 2 ∣ + C

\int (2 t + 1) d t

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

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

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

\frac{d y}{d x} = \frac{2 x + y + 1}{4 x + 2 y - 5}

What is the integral of (x-4)/(x+2) ?
The integral of (x-4)/(x+2) is x+2-6ln|x+2|+C