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

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

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

\frac{9}{17} x^{\frac{17}{9}} + C

Solution steps

assuming

x \geq 0

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

Apply the Power Rule

: \frac{9}{17} x^{\frac{17}{9}}

= \frac{9}{17} x^{\frac{17}{9}}

Add a constant to the solution

= \frac{9}{17} x^{\frac{17}{9}} + C

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\int \frac{x}{25 + 4 x ^{2}} d x

\frac{d}{d t} (\frac{k}{t})

\frac{d}{d x} (e^{x y} (y + x \frac{d y}{d x}))

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