What is the integral of-5x^{-1} ?

The integral of-5x^{-1} is -5ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-5x^{-1}

\int - 5 x^{- 1} d x

- 5 ln ∣ x ∣ + C

Solution steps

\int - 5 x^{- 1} d x

Take the constant out:

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

= - 5 \cdot \int x^{- 1} d x

Use the common integral:

\int x^{- 1} d x = ln (∣ x ∣)

= - 5 ln ∣ x ∣

Add a constant to the solution

= - 5 ln ∣ x ∣ + C

\int_{- \infty}^{4} \frac{1}{x ^{2} + 1} d x

(\frac{3 x ^{2} - 2}{2 x + 3})^{3}

\int (5 x^{2} + 6 x - 8) d x

\int \frac{( x ^{4} + 8 )}{x ^{3}} d x

\frac{8}{x}