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

The integral of 3\sqrt[3]{x^2} is 9/5 x^{5/3}+C

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

\frac{9}{5} 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

= 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

sin (tan (9 x))

\int \frac{1}{1 ^{2} + 2 x ^{2}} d x

\int \frac{x ^{3} - 5 x ^{2} + 3 x + 14}{x - 3} d x

f (x) = e^{- 3 x}, (0, 1)

\frac{d x}{d t} = 5 x (6 - x)

What is the integral of 3\sqrt[3]{x^2} ?
The integral of 3\sqrt[3]{x^2} is 9/5 x^{5/3}+C