What is the integral of \sqrt[5]{x^8} ?

The integral of \sqrt[5]{x^8} is 5/13 x^{13/5}+C

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integral of \sqrt[5]{x^8}

\int 5 x^{8} d x

\frac{5}{13} x^{\frac{13}{5}} + C

Solution steps

\int 5 x^{8} d x

5 x^{8} = x^{\frac{8}{5}},

assuming

x \geq 0

= \int x^{\frac{8}{5}} d x

Apply the Power Rule

: \frac{5}{13} x^{\frac{13}{5}}

= \frac{5}{13} x^{\frac{13}{5}}

Add a constant to the solution

= \frac{5}{13} x^{\frac{13}{5}} + C

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What is the integral of \sqrt[5]{x^8} ?
The integral of \sqrt[5]{x^8} is 5/13 x^{13/5}+C