What is the integral of 10x\sqrt[3]{x^2} ?

The integral of 10x\sqrt[3]{x^2} is 15/4 x^{8/3}+C

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integral of 10x\sqrt[3]{x^2}

\frac{15}{4} x^{\frac{8}{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

= 10 \cdot \int x x^{\frac{2}{3}} d x

Simplify

x x^{\frac{2}{3}} : x^{\frac{5}{3}}

= 10 \cdot \int x^{\frac{5}{3}} d x

Apply the Power Rule

= 10 \cdot \frac{3}{8} x^{\frac{8}{3}}

Simplify

10 \cdot \frac{3}{8} x^{\frac{8}{3}} : \frac{15}{4} x^{\frac{8}{3}}

= \frac{15}{4} x^{\frac{8}{3}}

Add a constant to the solution

= \frac{15}{4} x^{\frac{8}{3}} + C

What is the integral of 10x\sqrt[3]{x^2} ?
The integral of 10x\sqrt[3]{x^2} is 15/4 x^{8/3}+C