What is the integral of 8/9 x^{8/9} ?

The integral of 8/9 x^{8/9} is 8/17 x^{17/9}+C

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integral of 8/9 x^{8/9}

\int \frac{8}{9} x^{\frac{8}{9}} d x

\frac{8}{17} x^{\frac{17}{9}} + C

Solution steps

\int \frac{8}{9} x^{\frac{8}{9}} d x

Take the constant out:

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

= \frac{8}{9} \cdot \int x^{\frac{8}{9}} d x

Apply the Power Rule

: \frac{9}{17} x^{\frac{17}{9}}

= \frac{8}{9} \cdot \frac{9}{17} x^{\frac{17}{9}}

Simplify

\frac{8}{9} \cdot \frac{9}{17} x^{\frac{17}{9}} : \frac{8}{17} x^{\frac{17}{9}}

= \frac{8}{17} x^{\frac{17}{9}}

Add a constant to the solution

= \frac{8}{17} x^{\frac{17}{9}} + C

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What is the integral of 8/9 x^{8/9} ?
The integral of 8/9 x^{8/9} is 8/17 x^{17/9}+C