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

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

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integral of x/(sqrt(x))

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

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

Solution steps

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

Simplify

\frac{x}{x} : x

= \int x d x

Apply the Power Rule

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

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

Add a constant to the solution

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

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