What is the integral of 5x^{1/2} ?

The integral of 5x^{1/2} is 10/3 x^{3/2}+C

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integral of 5x^{1/2}

\int 5 x^{\frac{1}{2}} d x

\frac{10}{3} x^{\frac{3}{2}} + C

Solution steps

\int 5 x^{\frac{1}{2}} d x

Take the constant out:

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

= 5 \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

= 5 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

5 \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{10}{3} x^{\frac{3}{2}}

= \frac{10}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{10}{3} x^{\frac{3}{2}} + C