What is the integral of-1/9 x^{-10/9} ?

The integral of-1/9 x^{-10/9} is 1/(x^{1/9)}+C

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integral of-1/9 x^{-10/9}

\int - \frac{1}{9} x^{- \frac{10}{9}} d x

\frac{1}{x ^{\frac{1}{9}}} + C

Solution steps

\int - \frac{1}{9} x^{- \frac{10}{9}} d x

Take the constant out:

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

= - \frac{1}{9} \cdot \int x^{- \frac{10}{9}} d x

Apply the Power Rule

: - \frac{9}{x ^{\frac{1}{9}}}

= - \frac{1}{9} (- \frac{9}{x ^{\frac{1}{9}}})

Simplify

- \frac{1}{9} (- \frac{9}{x ^{\frac{1}{9}}}) : \frac{1}{x ^{\frac{1}{9}}}

= \frac{1}{x ^{\frac{1}{9}}}

Add a constant to the solution

= \frac{1}{x ^{\frac{1}{9}}} + C

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What is the integral of-1/9 x^{-10/9} ?
The integral of-1/9 x^{-10/9} is 1/(x^{1/9)}+C