What is the integral of 1/(x(50000-x)) ?

The integral of 1/(x(50000-x)) is 1/50000 ln|x|-1/50000 ln|x-50000|+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(50000-x))

\int \frac{1}{x ( 50000 - x )} d x

\frac{1}{50000} ln ∣ x ∣ - \frac{1}{50000} ln ∣ x - 50000 ∣ + C

Solution steps

\int \frac{1}{x ( 50000 - x )} d x

Take the partial fraction of

\frac{1}{x ( 50000 - x )} : \frac{1}{50000 x} - \frac{1}{50000 ( x - 50000 )}

= \int \frac{1}{50000 x} - \frac{1}{50000 ( x - 50000 )} 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}{50000 x} d x - \int \frac{1}{50000 ( x - 50000 )} d x

\int \frac{1}{50000 x} d x = \frac{1}{50000} ln ∣ x ∣

\int \frac{1}{50000 ( x - 50000 )} d x = \frac{1}{50000} ln ∣ x - 50000 ∣

= \frac{1}{50000} ln ∣ x ∣ - \frac{1}{50000} ln ∣ x - 50000 ∣

Add a constant to the solution

= \frac{1}{50000} ln ∣ x ∣ - \frac{1}{50000} ln ∣ x - 50000 ∣ + C

\int cosh (10 x) d x

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

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

\int \frac{49}{x ^{2} 49 - x ^{2}} d x

\int r sin (r) d r

What is the integral of 1/(x(50000-x)) ?
The integral of 1/(x(50000-x)) is 1/50000 ln|x|-1/50000 ln|x-50000|+C