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

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

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integral of (x^{-2})/3

integral

\frac{x ^{- 2}}{3}

- \frac{1}{3 x} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

= \frac{1}{3} (- \frac{1}{x})

Simplify

\frac{1}{3} (- \frac{1}{x}) : - \frac{1}{3 x}

= - \frac{1}{3 x}

Add a constant to the solution

= - \frac{1}{3 x} + C