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

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

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integral of 3x^{-2/3}

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

9 x^{\frac{1}{3}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

= 9 x^{\frac{1}{3}}

Add a constant to the solution

= 9 x^{\frac{1}{3}} + C