What is the integral of 4/5 x^{4/5} ?

The integral of 4/5 x^{4/5} is 4/9 x^{9/5}+C

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integral of 4/5 x^{4/5}

\int \frac{4}{5} x^{\frac{4}{5}} d x

\frac{4}{9} x^{\frac{9}{5}} + C

Solution steps

\int \frac{4}{5} x^{\frac{4}{5}} d x

Take the constant out:

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

= \frac{4}{5} \cdot \int x^{\frac{4}{5}} d x

Apply the Power Rule

= \frac{4}{5} \cdot \frac{5}{9} x^{\frac{9}{5}}

Simplify

\frac{4}{5} \cdot \frac{5}{9} x^{\frac{9}{5}} : \frac{4}{9} x^{\frac{9}{5}}

= \frac{4}{9} x^{\frac{9}{5}}

Add a constant to the solution

= \frac{4}{9} x^{\frac{9}{5}} + C

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What is the integral of 4/5 x^{4/5} ?
The integral of 4/5 x^{4/5} is 4/9 x^{9/5}+C