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

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

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integral of sqrt(x/2)

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

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

Solution steps

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

Simplify

\frac{x}{2} : \frac{x}{2}

= \int \frac{x}{2} 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 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{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

f (x) = 3 x^{2} + 9 x^{3} - 5 x, at x = - 4

\frac{1}{2 ( s + 2 )}

x + 3

\frac{d}{d s} (\frac{3}{s ^{2} + 9})

\int arctan (x) d x

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