What is the integral of 5\sqrt[5]{x} ?

The integral of 5\sqrt[5]{x} is 25/6 x^{6/5}+C

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integral of 5\sqrt[5]{x}

\int 5 5 x d x

\frac{25}{6} x^{\frac{6}{5}} + C

Solution steps

\int 5 5 x d x

Take the constant out:

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

= 5 \cdot \int 5 x d x

Apply the Power Rule

: \frac{5}{6} x^{\frac{6}{5}}

= 5 \cdot \frac{5}{6} x^{\frac{6}{5}}

Simplify

5 \cdot \frac{5}{6} x^{\frac{6}{5}} : \frac{25}{6} x^{\frac{6}{5}}

= \frac{25}{6} x^{\frac{6}{5}}

Add a constant to the solution

= \frac{25}{6} x^{\frac{6}{5}} + C

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What is the integral of 5\sqrt[5]{x} ?
The integral of 5\sqrt[5]{x} is 25/6 x^{6/5}+C