en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(x-1)

Solution

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

Solution

ln ∣ x - 1 ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x - 1

= ln ∣ x - 1 ∣

Add a constant to the solution

= ln ∣ x - 1 ∣ + C

Popular Examples

derivative of (x^3-5x)(4x^2-3x)derivative of

(x^{3} - 5 x) (4 x^{2} - 3 x)

laplacetransform x+k*x laplace transform

x + k \cdot x

derivative of (2-3x/(7-x))

\frac{d}{d x} (\frac{2 - 3 x}{7 - x})

integral of (e^xcos(y)-x-2)

\int (e^{x} cos (y) - x - 2) d y

integral of f^2(x)

\int f^{2} (x) d x

Frequently Asked Questions (FAQ)

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