What is the integral of 2/(x-1) ?

The integral of 2/(x-1) is 2ln|x-1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 2/(x-1)

\int \frac{2}{x - 1} d x

2 ln ∣ x - 1 ∣ + C

Solution steps

\int \frac{2}{x - 1} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{x - 1} d x

Apply u-substitution

= 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = x - 1

= 2 ln ∣ x - 1 ∣

Add a constant to the solution

= 2 ln ∣ x - 1 ∣ + C