What is the integral of 1/2 sqrt(u) ?

The integral of 1/2 sqrt(u) is 1/3 u^{3/2}+C

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integral of 1/2 sqrt(u)

\int \frac{1}{2} u d u

\frac{1}{3} u^{\frac{3}{2}} + C

Solution steps

\int \frac{1}{2} u d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u d u

Apply the Power Rule

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

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

Simplify

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

= \frac{1}{3} u^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{3} u^{\frac{3}{2}} + C

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What is the integral of 1/2 sqrt(u) ?
The integral of 1/2 sqrt(u) is 1/3 u^{3/2}+C