What is the integral of 1/(x(10000-x)) ?

The integral of 1/(x(10000-x)) is 1/10000 ln|x|-1/10000 ln|x-10000|+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(10000-x))

\int \frac{1}{x ( 10000 - x )} d x

\frac{1}{10000} ln ∣ x ∣ - \frac{1}{10000} ln ∣ x - 10000 ∣ + C

Solution steps

\int \frac{1}{x ( 10000 - x )} d x

Take the partial fraction of

\frac{1}{x ( 10000 - x )} : \frac{1}{10000 x} - \frac{1}{10000 ( x - 10000 )}

= \int \frac{1}{10000 x} - \frac{1}{10000 ( x - 10000 )} 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}{10000 x} d x - \int \frac{1}{10000 ( x - 10000 )} d x

\int \frac{1}{10000 x} d x = \frac{1}{10000} ln ∣ x ∣

\int \frac{1}{10000 ( x - 10000 )} d x = \frac{1}{10000} ln ∣ x - 10000 ∣

= \frac{1}{10000} ln ∣ x ∣ - \frac{1}{10000} ln ∣ x - 10000 ∣

Add a constant to the solution

= \frac{1}{10000} ln ∣ x ∣ - \frac{1}{10000} ln ∣ x - 10000 ∣ + C

\int \frac{x ^{5}}{x ^{2} 9 x ^{2} + 9} d x

\int \frac{x ^{3}}{x ^{8} + 4} d x

\int e^{- 6 x + 5} d x

\int 2 y^{4} d y

\int \frac{1}{( 3 x + 5 ) ^{2}} d x

What is the integral of 1/(x(10000-x)) ?
The integral of 1/(x(10000-x)) is 1/10000 ln|x|-1/10000 ln|x-10000|+C