What is the integral of 8/9 x^{-1/9} ?

The integral of 8/9 x^{-1/9} is x^{8/9}+C

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integral of 8/9 x^{-1/9}

\int \frac{8}{9} x^{- \frac{1}{9}} d x

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

Solution steps

\int \frac{8}{9} x^{- \frac{1}{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{1}{9}} d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

x \to 3 lim (3 x)

\int \frac{1}{9} x^{2} d x

\frac{d}{d x} (\frac{( 4 x ^{3} + 2 x ^{2} )}{sin ( x )})^{2}

y = \frac{- 2 x ^{2} + 3 x - 15}{x ^{3} - 9 x}, x = 1, x = 2

\int sin (\frac{2 x}{3}) d x

What is the integral of 8/9 x^{-1/9} ?
The integral of 8/9 x^{-1/9} is x^{8/9}+C