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

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

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

- ln ∣ x - 2 ∣ + C

Solution steps

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

Take the constant out:

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

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

= - ln ∣ x - 2 ∣

Add a constant to the solution

= - ln ∣ x - 2 ∣ + C

\int 4 x^{3} + e^{x} + 1 d x

F (x) = 4 x^{6} (x^{4} - 6 x)

\int (5 x^{3} + 2 x^{2} - 2 x + 1) d x

\frac{x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

\frac{d}{d x} (\frac{2 π}{x})