What is the integral of (1/(2sqrt(x))) ?

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

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integral of (1/(2sqrt(x)))

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

x + C

Solution steps

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

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}{x} d x

Apply the Power Rule

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

Simplify

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

= x

Add a constant to the solution

= x + C

a re a y = 3 x, x = 0, x = 4

x d y - y d x = 2 x^{2} y^{2} d y, y (1) = 2

\frac{d}{d x} (cos (2 x) cos (x))

\int \frac{8 - 3 x}{25 - 64 x ^{2}} d x

d er i v a t i v e (x - 3) (x^{2} + 6)

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