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

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

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integral of (-2sqrt(x))/3

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

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

Solution steps

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

Simplify

= (- \frac{2}{3}) \cdot \int x d x

Apply the Power Rule

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

= (- \frac{2}{3}) \frac{2}{3} x^{\frac{3}{2}}

Simplify

(- \frac{2}{3}) \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

y^{^{''}} - 9 y^{^{'}} = 1 + 3 e^{2 x}

\frac{d y}{d x} = \frac{y}{x + 1}

t \to 0 lim (sin (5 t))

\frac{d}{d x} (- 10 sin (2 x))

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

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