What is the integral of 8\sqrt[4]{x} ?

The integral of 8\sqrt[4]{x} is 32/5 x^{5/4}+C

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integral of 8\sqrt[4]{x}

\frac{32}{5} x^{\frac{5}{4}} + C

Solution steps

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply the Power Rule

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

= 8 \cdot \frac{4}{5} x^{\frac{5}{4}}

Simplify

8 \cdot \frac{4}{5} x^{\frac{5}{4}} : \frac{32}{5} x^{\frac{5}{4}}

= \frac{32}{5} x^{\frac{5}{4}}

Add a constant to the solution

= \frac{32}{5} x^{\frac{5}{4}} + C

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What is the integral of 8\sqrt[4]{x} ?
The integral of 8\sqrt[4]{x} is 32/5 x^{5/4}+C