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

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

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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 x ^{2}}

= \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

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