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

Take the constant out:

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

= - \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) = - 4

\frac{\partial}{\partial x} (e^{- s i n^{2} (x)} (x + c))

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

\frac{d}{d x} ((x + 6)^{\frac{2}{3}})

y^{^{''}} + 25 y = 0.5 sin (5 t), y (0) = 0, y^{^{'}} (0) = 0