What is the integral of-1/3 x^{-4/3} ?

The integral of-1/3 x^{-4/3} is 1/(x^{1/3)}+C

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integral of-1/3 x^{-4/3}

\int - \frac{1}{3} x^{- \frac{4}{3}} d x

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

Solution steps

\int - \frac{1}{3} x^{- \frac{4}{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{4}{3}} d x

Apply the Power Rule

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

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

Simplify

- \frac{1}{3} (- \frac{3}{x ^{\frac{1}{3}}}) : \frac{1}{x ^{\frac{1}{3}}}

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

Add a constant to the solution

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

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What is the integral of-1/3 x^{-4/3} ?
The integral of-1/3 x^{-4/3} is 1/(x^{1/3)}+C