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

Popular >

integral of 2x^{-1}

integral

2 x^{- 1}

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

\int \frac{x + 2}{7 - 9 x ^{2}} d x

\int sin^{4} (x) x d x

\int 4 x^{3} x^{4} + 7 d x

\int \frac{3 x ^{2} + 1}{x ^{2} - 4 x + 8} d x

\int \frac{u ^{2}}{a ^{2} + u ^{2}} d u