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

The integral of-x^{-1} 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-x^{-1}

\int - x^{- 1} d x

- ln ∣ x ∣ + C

Solution steps

\int - x^{- 1} d x

Take the constant out:

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

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

Use the common integral:

\int x^{- 1} d x = ln (∣ x ∣)

= - ln ∣ x ∣

Add a constant to the solution

= - ln ∣ x ∣ + C

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

x \to \frac{π}{6} lim (sin (2 x - π))

\int x^{2} - 9 x + 5 d x

\frac{d}{d t} (e^{t} (a cos (2 t) + b sin (2 t)))

\int \frac{x}{x ^{3}} d x