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

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

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

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

u^{\frac{1}{2}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: 2 u^{\frac{1}{2}}

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

Simplify

\frac{1}{2} \cdot 2 u^{\frac{1}{2}} : u^{\frac{1}{2}}

= u^{\frac{1}{2}}

Add a constant to the solution

= u^{\frac{1}{2}} + C

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