What is the integral of 5pi\sqrt[3]{x^2} ?

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

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integral of 5pi\sqrt[3]{x^2}

3 π x^{\frac{5}{3}} + 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

= 5 π \cdot \int x^{\frac{2}{3}} d x

Apply the Power Rule

: \frac{3}{5} x^{\frac{5}{3}}

= 5 π \frac{3}{5} x^{\frac{5}{3}}

Simplify

5 π \frac{3}{5} x^{\frac{5}{3}} : 3 π x^{\frac{5}{3}}

= 3 π x^{\frac{5}{3}}

Add a constant to the solution

= 3 π x^{\frac{5}{3}} + C

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