What is the integral of 3x^{2/3} ?

The integral of 3x^{2/3} is 9/5 x^{5/3}+C

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integral of 3x^{2/3}

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

\frac{9}{5} x^{\frac{5}{3}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

3 \cdot \frac{3}{5} x^{\frac{5}{3}} : \frac{9}{5} x^{\frac{5}{3}}

= \frac{9}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{9}{5} x^{\frac{5}{3}} + C

- \frac{3}{x ^{3}}

\int (\frac{d y}{1})^{2} d x

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

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

\frac{d x}{d t} = x - x^{2}