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

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

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{1}{5 x ^{5}} d x

f (x) = \frac{1}{3 x ^{2} + 4 x}

\frac{\partial}{\partial z} (\frac{( 3 x + y )}{z})

\frac{d y}{d t} = - y + 5

y^{^{''}} + 9 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

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