What is the integral of x*\sqrt[4]{x^9} ?

The integral of x*\sqrt[4]{x^9} is 4/17 x^{17/4}+C

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integral of x*\sqrt[4]{x^9}

\frac{4}{17} x^{\frac{17}{4}} + C

Solution steps

assuming

x \geq 0

= \int x x^{\frac{9}{4}} d x

Simplify

x x^{\frac{9}{4}} : x^{\frac{13}{4}}

= \int x^{\frac{13}{4}} d x

Apply the Power Rule

: \frac{4}{17} x^{\frac{17}{4}}

= \frac{4}{17} x^{\frac{17}{4}}

Add a constant to the solution

= \frac{4}{17} x^{\frac{17}{4}} + C

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What is the integral of x*\sqrt[4]{x^9} ?
The integral of x*\sqrt[4]{x^9} is 4/17 x^{17/4}+C