What is the integral of 1/(4sqrt(x)) ?

The integral of 1/(4sqrt(x)) is 1/2 sqrt(x)+C

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integral of 1/(4sqrt(x))

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

\frac{1}{2} x + C

Solution steps

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

Apply the Power Rule

= \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} x

Add a constant to the solution

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

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