What is the integral of 2y^{-1} ?

The integral of 2y^{-1} is 2ln|y|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2y^{-1}

\int 2 y^{- 1} d y

2 ln ∣ y ∣ + C

Solution steps

\int 2 y^{- 1} d y

Take the constant out:

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

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

Use the common integral:

\int y^{- 1} d y = ln (∣ y ∣)

= 2 ln ∣ y ∣

Add a constant to the solution

= 2 ln ∣ y ∣ + C

\int (\frac{6 x + 1}{3 3 x + 2}) d x

\int \frac{1}{5 y + 8} d y

\int \frac{1}{x ^{2} + 4} + cos (2 x) d x

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

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