What is the integral of 4\sqrt[5]{x^3} ?

The integral of 4\sqrt[5]{x^3} is 5/2 x^{8/5}+C

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integral of 4\sqrt[5]{x^3}

\frac{5}{2} x^{\frac{8}{5}} + C

Solution steps

Take the constant out:

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

assuming

x \geq 0

= 4 \cdot \int x^{\frac{3}{5}} d x

Apply the Power Rule

: \frac{5}{8} x^{\frac{8}{5}}

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

Simplify

4 \cdot \frac{5}{8} x^{\frac{8}{5}} : \frac{5}{2} x^{\frac{8}{5}}

= \frac{5}{2} x^{\frac{8}{5}}

Add a constant to the solution

= \frac{5}{2} x^{\frac{8}{5}} + C

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What is the integral of 4\sqrt[5]{x^3} ?
The integral of 4\sqrt[5]{x^3} is 5/2 x^{8/5}+C