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

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

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

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

f (x) = \frac{7 x + 4}{x + 70}

\int \frac{3}{25 - x ^{2}} d x

\frac{d}{d x} (arcsec (x))

y^{^{''}} + x^{2} y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 2

f (x) = \frac{x}{x + 5}