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

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

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integral of sqrt(y/3)

\int \frac{y}{3} d y

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

Solution steps

\int \frac{y}{3} d y

Simplify

\frac{y}{3} : \frac{y}{3}

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

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

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

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

Add a constant to the solution

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

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