What is the integral of (5x)/(x(x-1)) ?

The integral of (5x)/(x(x-1)) is 5ln|x-1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5x)/(x(x-1))

\int \frac{5 x}{x ( x - 1 )} d x

5 ln ∣ x - 1 ∣ + C

Solution steps

\int \frac{5 x}{x ( x - 1 )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{x}{x ( x - 1 )} d x

Apply u-substitution

: \int \frac{1}{u} d u

= 5 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 ln ∣ u ∣

Substitute back

u = x - 1

= 5 ln ∣ x - 1 ∣

Add a constant to the solution

= 5 ln ∣ x - 1 ∣ + C

\int 11 ln (x) d x

\frac{2}{( s + 2 ) ^{2}}

\frac{d}{d x} (\frac{2 x}{9 - cot ( x )})

(3 x^{2} - 6 x y) d x - (3 x^{2} + 2 y) d y = 0

x \to π lim (x + sin (x))

What is the integral of (5x)/(x(x-1)) ?
The integral of (5x)/(x(x-1)) is 5ln|x-1|+C