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

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

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integral of 3x^{-1/3}

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

\frac{9}{2} x^{\frac{2}{3}} + C

Solution steps

\int 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

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

Apply the Power Rule

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

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

Simplify

3 \cdot \frac{3}{2} x^{\frac{2}{3}} : \frac{9}{2} x^{\frac{2}{3}}

= \frac{9}{2} x^{\frac{2}{3}}

Add a constant to the solution

= \frac{9}{2} x^{\frac{2}{3}} + C

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