What is the integral of 2/3 sqrt(x) ?

The integral of 2/3 sqrt(x) is 4/9 x^{3/2}+C

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integral of 2/3 sqrt(x)

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

\frac{4}{9} x^{\frac{3}{2}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{2}{3} x^{\frac{3}{2}}

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

Simplify

\frac{2}{3} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{4}{9} x^{\frac{3}{2}}

= \frac{4}{9} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{4}{9} x^{\frac{3}{2}} + C

\frac{d}{d x} (14 x)

t^{2} y^{^{'}} + t y = 4, y (1) = 3

x \to 3 lim (2 x^{3} - 4 x^{2} + x - 7)

\frac{\partial}{\partial x} (tan (3 x^{2} + 2 x))

What is the integral of 2/3 sqrt(x) ?
The integral of 2/3 sqrt(x) is 4/9 x^{3/2}+C