What is the integral of 1/2 x^{-3} ?

The integral of 1/2 x^{-3} is -1/(4x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/2 x^{-3}

\int \frac{1}{2} x^{- 3} d x

- \frac{1}{4 x ^{2}} + C

Solution steps

\int \frac{1}{2} x^{- 3} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int x^{- 3} d x

Apply the Power Rule

= \frac{1}{2} (- \frac{1}{2 x ^{2}})

Simplify

\frac{1}{2} (- \frac{1}{2 x ^{2}}) : - \frac{1}{4 x ^{2}}

= - \frac{1}{4 x ^{2}}

Add a constant to the solution

= - \frac{1}{4 x ^{2}} + C