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

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

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

2 ln ∣ x - 2 ∣ + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = x - 2

= 2 ln ∣ x - 2 ∣

Add a constant to the solution

= 2 ln ∣ x - 2 ∣ + C

\int arccsc (\frac{x}{2}) d x

y^{^{''}} - 8 y^{^{'}} + 13 y = 0

n \to \infty lim (1 - n^{2})

\frac{\partial}{\partial x} (- 7 (x + 2 y)^{5})

\int \frac{1}{y ^{\frac{2}{3}}} d y