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

The integral of 10\sqrt[3]{x^2} is 6x^{5/3}+C

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

\int 10 3 x^{2} d x

6 x^{\frac{5}{3}} + C

Solution steps

\int 10 3 x^{2} d x

Take the constant out:

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

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

3 x^{2} = x^{\frac{2}{3}},

assuming

x \geq 0

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

Apply the Power Rule

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

Simplify

10 \cdot \frac{3}{5} x^{\frac{5}{3}} : 6 x^{\frac{5}{3}}

= 6 x^{\frac{5}{3}}

Add a constant to the solution

= 6 x^{\frac{5}{3}} + C

\frac{\partial}{\partial x} (- e^{x} sin (y))

\frac{d}{d x} (e^{x} sin (6 x))

\int x^{2} x + 3 d x

t a y l or cos (2 x)

\frac{\partial}{\partial z} (x^{2} + 2 y + 2 z)

What is the integral of 10\sqrt[3]{x^2} ?
The integral of 10\sqrt[3]{x^2} is 6x^{5/3}+C