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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((-1)/x)

\int (\frac{- 1}{x}) d x

- ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - ln ∣ x ∣

Add a constant to the solution

= - ln ∣ x ∣ + C

\int (t e^{t}) d t

\int - 8 x sin (4 x^{2} - 3) d x

\int (10 x^{4} - 3 x^{2} + \frac{4}{x}) d x

\int 6 cos (x) + sec^{2} (x) d x

\int x^{35} d x