What is the integral of 1/(x(x-7)) ?

The integral of 1/(x(x-7)) is -1/7 ln|x|+1/7 ln|x-7|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(x(x-7))

\int \frac{1}{x ( x - 7 )} d x

- \frac{1}{7} ln ∣ x ∣ + \frac{1}{7} ln ∣ x - 7 ∣ + C

Solution steps

\int \frac{1}{x ( x - 7 )} d x

Take the partial fraction of

\frac{1}{x ( x - 7 )} : - \frac{1}{7 x} + \frac{1}{7 ( x - 7 )}

= \int - \frac{1}{7 x} + \frac{1}{7 ( x - 7 )} 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}{7 x} d x + \int \frac{1}{7 ( x - 7 )} d x

\int \frac{1}{7 x} d x = \frac{1}{7} ln ∣ x ∣

\int \frac{1}{7 ( x - 7 )} d x = \frac{1}{7} ln ∣ x - 7 ∣

= - \frac{1}{7} ln ∣ x ∣ + \frac{1}{7} ln ∣ x - 7 ∣

Add a constant to the solution

= - \frac{1}{7} ln ∣ x ∣ + \frac{1}{7} ln ∣ x - 7 ∣ + C

\frac{d}{d y} (\frac{1}{1 + y ^{2}})

\frac{\partial}{\partial v} (u + uv)

y = x^{3} - 8 x^{2} + 4 x - 32

\int \frac{1}{sin ( y )} d y

\int sin (x) sec (x) d x

What is the integral of 1/(x(x-7)) ?
The integral of 1/(x(x-7)) is -1/7 ln|x|+1/7 ln|x-7|+C