What is the integral of (3x^{1/3}) ?

The integral of (3x^{1/3}) is 9/4 x^{4/3}+C

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integral of (3x^{1/3})

\int (3 x^{\frac{1}{3}}) d x

\frac{9}{4} x^{\frac{4}{3}} + C

Solution steps

\int 3 x^{\frac{1}{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{1}{3}} d x

Apply the Power Rule

: \frac{3}{4} x^{\frac{4}{3}}

= 3 \cdot \frac{3}{4} x^{\frac{4}{3}}

Simplify

3 \cdot \frac{3}{4} x^{\frac{4}{3}} : \frac{9}{4} x^{\frac{4}{3}}

= \frac{9}{4} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{9}{4} x^{\frac{4}{3}} + C

\int (e^{3 x + 9} - 3 x^{2}) d x

y = 8 arcsin (\frac{x}{4}) - \frac{x 16 - x ^{2}}{2}

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

\int_{- 1}^{1} 9 x^{2} + 6 x - 3 d x

\frac{\partial}{\partial x} (3 x^{2} - 3 y)

What is the integral of (3x^{1/3}) ?
The integral of (3x^{1/3}) is 9/4 x^{4/3}+C