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

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

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integral of 1/(4x^{1/2)}

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

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

Solution steps

\int \frac{1}{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

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

Apply the Power Rule

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

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

Simplify

\frac{1}{4} \cdot 2 x^{\frac{1}{2}} : \frac{1}{2} x^{\frac{1}{2}}

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

Add a constant to the solution

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

x^{2} y^{^{''}} - x (x + 2) y^{^{'}} + (x + 2) y = 0

x + 7 x - 7

x \to \infty lim (3 + x)

9 y^{^{''}} + 6 y^{^{'}} + y = e^{- \frac{1}{3} t}

\frac{d}{d x} (\frac{1}{x ^{2} x})

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