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

The integral of 2/(x^{1/2)} is 4x^{1/2}+C

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

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

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

Solution steps

\int \frac{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

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

Apply the Power Rule

= 2 \cdot 2 x^{\frac{1}{2}}

Simplify

= 4 x^{\frac{1}{2}}

Add a constant to the solution

= 4 x^{\frac{1}{2}} + C