What is the integral of 4x^{1/2} ?

The integral of 4x^{1/2} is 8/3 x^{3/2}+C

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integral of 4x^{1/2}

\int 4 x^{\frac{1}{2}} d x

\frac{8}{3} x^{\frac{3}{2}} + C

Solution steps

\int 4 x^{\frac{1}{2}} d x

Take the constant out:

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

= 4 \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

= 4 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

4 \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{8}{3} x^{\frac{3}{2}}

= \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{8}{3} x^{\frac{3}{2}} + C