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

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

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integral of u/(sqrt(u))

\int \frac{u}{u} d u

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

Solution steps

\int \frac{u}{u} d u

Simplify

\frac{u}{u} : u

= \int u d u

Apply the Power Rule

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

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

Add a constant to the solution

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

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