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

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

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integral of sqrt(x/3)

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

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

Solution steps

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

Simplify

\frac{x}{3} : \frac{x}{3}

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

Take the constant out:

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

= \frac{1}{3} \cdot \int x d x

Apply the Power Rule

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

= \frac{1}{3} \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

\frac{1}{3} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{2}{3 3} x^{\frac{3}{2}}

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

Add a constant to the solution

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

y^{^{''}} + 3 y = - 9

- 2 cot (x) csc (x)

x \to 2 π lim (\frac{1}{sin ( x )})

sin (2 x)

\frac{d}{d x} (\frac{x ^{4} - 4 x + 3}{x + 1})

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