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

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

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

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

x^{\frac{2}{3}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

= \frac{2}{3} \cdot \frac{3}{2} x^{\frac{2}{3}}

Simplify

\frac{2}{3} \cdot \frac{3}{2} x^{\frac{2}{3}} : x^{\frac{2}{3}}

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

Add a constant to the solution

= x^{\frac{2}{3}} + C

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