What is the integral of 2/5 x^{-1/5} ?

The integral of 2/5 x^{-1/5} is 1/2 x^{4/5}+C

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integral of 2/5 x^{-1/5}

\int \frac{2}{5} x^{- \frac{1}{5}} d x

\frac{1}{2} x^{\frac{4}{5}} + C

Solution steps

\int \frac{2}{5} x^{- \frac{1}{5}} d x

Take the constant out:

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

= \frac{2}{5} \cdot \int x^{- \frac{1}{5}} d x

Apply the Power Rule

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

= \frac{2}{5} \cdot \frac{5}{4} x^{\frac{4}{5}}

Simplify

\frac{2}{5} \cdot \frac{5}{4} x^{\frac{4}{5}} : \frac{1}{2} x^{\frac{4}{5}}

= \frac{1}{2} x^{\frac{4}{5}}

Add a constant to the solution

= \frac{1}{2} x^{\frac{4}{5}} + C

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What is the integral of 2/5 x^{-1/5} ?
The integral of 2/5 x^{-1/5} is 1/2 x^{4/5}+C