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

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

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

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

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

Solution steps

\int \frac{1}{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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

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