What is the integral of x/(2sqrt(x)) ?

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

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integral of x/(2sqrt(x))

\int \frac{x}{2 x} d x

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

Solution steps

\int \frac{x}{2 x} d x

Take the constant out:

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

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

Simplify

\frac{x}{x} : x

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

x \to \infty lim (\frac{x}{k})

\frac{d}{d x} (6 x^{2} - x)

\frac{\partial}{\partial y} (x sin (yz))

x^{2} - x

x \to 0 lim (\frac{∣ x ∣}{2 x})

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