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

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

Popular >

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

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

\frac{1}{4} ln ∣ x ∣ - \frac{1}{4} ln ∣ x + 4 ∣ + C

Solution steps

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

Take the partial fraction of

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

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

\int \frac{1}{4 x} d x = \frac{1}{4} ln ∣ x ∣

\int \frac{1}{4 ( x + 4 )} d x = \frac{1}{4} ln ∣ x + 4 ∣

= \frac{1}{4} ln ∣ x ∣ - \frac{1}{4} ln ∣ x + 4 ∣

Add a constant to the solution

= \frac{1}{4} ln ∣ x ∣ - \frac{1}{4} ln ∣ x + 4 ∣ + C

\frac{d ^{2}}{d x ^{2}} (e^{\frac{1}{x}})

\frac{d y}{d x} = \frac{y}{x ^{2}}, y (1) = 2

arctan (sin (2 x))

f (x) = x, at x = \frac{1}{81}

5 \frac{1}{x}

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