What is the integral of (2x^{-1}) ?

The integral of (2x^{-1}) is 2ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2x^{-1})

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

2 ln ∣ x ∣ + C

Solution steps

\int 2 x^{- 1} d x

Take the constant out:

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

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

Use the common integral:

\int x^{- 1} d x = ln (∣ x ∣)

= 2 ln ∣ x ∣

Add a constant to the solution

= 2 ln ∣ x ∣ + C

2 y^{^{''}} + y^{^{'}} - 3 y = 0

y^{^{'}} = \frac{y}{4 x}

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2} - 20)

d er i v a t i v e \frac{y}{3}

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