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

The integral of x\sqrt[4]{x^5} is 4/13 x^{13/4}+C

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

\int x 4 x^{5} d x

\frac{4}{13} x^{\frac{13}{4}} + C

Solution steps

\int x 4 x^{5} d x

4 x^{5} = x^{\frac{5}{4}},

assuming

x \geq 0

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

Simplify

x x^{\frac{5}{4}} : x^{\frac{9}{4}}

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

Apply the Power Rule

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

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

Add a constant to the solution

= \frac{4}{13} x^{\frac{13}{4}} + C

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What is the integral of x\sqrt[4]{x^5} ?
The integral of x\sqrt[4]{x^5} is 4/13 x^{13/4}+C