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

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

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

\int 3 x^{2} d x

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

Solution steps

\int 3 x^{2} d x

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

assuming

x \geq 0

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

Apply the Power Rule

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

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (x cos (z))

7 x^{2} - 9 x, at x = - 17

f (x) = 2 x^{2} - 5 x + 3, at x = 1

\int \frac{( 3 + 4 x )}{3 x - x ^{2} - 2} d x

x \to 3 lim (\frac{x + 3}{x + 6})

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