What is the integral of 1/2 x^{1/2} ?

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

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integral of 1/2 x^{1/2}

\int \frac{1}{2} x^{\frac{1}{2}} d x

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

Solution steps

\int \frac{1}{2} x^{\frac{1}{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^{\frac{1}{2}} 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 4 lim (x^{2} - 3 x + 7)

x \to 3 lim (0)

ln (ln (9 s))

- t^{2} + 2 t + 4

\frac{d y}{d x} = \frac{1}{1 + x ^{2}}

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