What is the integral of \sqrt[8]{x^9} ?

The integral of \sqrt[8]{x^9} is 8/17 x^{17/8}+C

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integral of \sqrt[8]{x^9}

\frac{8}{17} x^{\frac{17}{8}} + C

Solution steps

assuming

x \geq 0

= \int x^{\frac{9}{8}} d x

Apply the Power Rule

: \frac{8}{17} x^{\frac{17}{8}}

= \frac{8}{17} x^{\frac{17}{8}}

Add a constant to the solution

= \frac{8}{17} x^{\frac{17}{8}} + C

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What is the integral of \sqrt[8]{x^9} ?
The integral of \sqrt[8]{x^9} is 8/17 x^{17/8}+C