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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(1-x)

integral

\frac{1}{1 - x}

- ln ∣ 1 - x ∣ + C

Solution steps

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

Apply u-substitution

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

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = 1 - x

= - ln ∣ 1 - x ∣

Add a constant to the solution

= - ln ∣ 1 - x ∣ + C

\int \frac{1}{x - 20} d x

\int \frac{e ^{2 x} + 1}{e ^{x} + 1} d x

\int sin (2 x) sin (3 x) cos (4 x) d x

\int \frac{1}{x ^{2} + 3 x - 10} d x

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