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

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

Popular >

integral of (sqrt(x))/2

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

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

Solution steps

\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{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

y^{^{''}} + 5 y + \frac{349}{4} y = 0, y (0) = - 5, y^{^{'}} (0) = - \frac{29}{2}

\frac{d}{d x} ((x^{3} + 2)^{3})

\int_{- 1}^{1} \frac{x}{x ^{2} + 25} d x

\frac{\partial}{\partial z} (y^{2} e^{x yz})

\int_{1}^{\infty} \frac{1}{x ^{2} + 4} d x

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