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

The integral of 1/(3x^{-2)} is (x^3)/9+C

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integral of 1/(3x^{-2)}

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

\frac{x ^{3}}{9} + C

Solution steps

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{1}{3} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{3} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{9}

= \frac{x ^{3}}{9}

Add a constant to the solution

= \frac{x ^{3}}{9} + C

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