What is the integral of (-1)/y ?

The integral of (-1)/y is -ln|y|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (-1)/y

\int \frac{- 1}{y} d y

- ln ∣ y ∣ + C

Solution steps

\int \frac{- 1}{y} d y

Take the constant out:

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

= - \int \frac{1}{y} d y

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= - ln ∣ y ∣

Add a constant to the solution

= - ln ∣ y ∣ + C

n \to \infty lim (∣ an ∣)

k = 1 \sum \infty \frac{1}{4 ^{k + 1}}

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

\frac{d}{d x} (2 x^{8})

\int x^{2} + x^{3} d x