What is the integral of 1/9 x^{-7/9} ?

The integral of 1/9 x^{-7/9} is 1/2 x^{2/9}+C

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integral of 1/9 x^{-7/9}

\int \frac{1}{9} x^{- \frac{7}{9}} d x

\frac{1}{2} x^{\frac{2}{9}} + C

Solution steps

\int \frac{1}{9} x^{- \frac{7}{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{7}{9}} d x

Apply the Power Rule

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

= \frac{1}{9} \cdot \frac{9}{2} x^{\frac{2}{9}}

Simplify

\frac{1}{9} \cdot \frac{9}{2} x^{\frac{2}{9}} : \frac{1}{2} x^{\frac{2}{9}}

= \frac{1}{2} x^{\frac{2}{9}}

Add a constant to the solution

= \frac{1}{2} x^{\frac{2}{9}} + C

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What is the integral of 1/9 x^{-7/9} ?
The integral of 1/9 x^{-7/9} is 1/2 x^{2/9}+C