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

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

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

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

- 3 (2 - x)^{\frac{1}{3}} + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{u ^{\frac{2}{3}}} d u

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

Take the constant out:

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

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

Apply the Power Rule

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

= - 3 u^{\frac{1}{3}}

Substitute back

u = 2 - x

= - 3 (2 - x)^{\frac{1}{3}}

Add a constant to the solution

= - 3 (2 - x)^{\frac{1}{3}} + C

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