What is the integral of 2/(\sqrt[5]{x)} ?

The integral of 2/(\sqrt[5]{x)} is 5/2 x^{4/5}+C

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integral of 2/(\sqrt[5]{x)}

\int \frac{2}{5 x} d x

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

Solution steps

\int \frac{2}{5 x} d x

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

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What is the integral of 2/(\sqrt[5]{x)} ?
The integral of 2/(\sqrt[5]{x)} is 5/2 x^{4/5}+C