What is the integral of \sqrt[4]{x^5} ?

The integral of \sqrt[4]{x^5} is 4/9 x^{9/4}+C

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integral of \sqrt[4]{x^5}

\frac{4}{9} x^{\frac{9}{4}} + C

Solution steps

assuming

x \geq 0

= \int x^{\frac{5}{4}} d x

Apply the Power Rule

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

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

Add a constant to the solution

= \frac{4}{9} x^{\frac{9}{4}} + C

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What is the integral of \sqrt[4]{x^5} ?
The integral of \sqrt[4]{x^5} is 4/9 x^{9/4}+C