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

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

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

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

x + C

Solution steps

\int \frac{x}{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{x}{x} d x

Simplify

\frac{x}{x} : \frac{1}{x}

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

Apply the Power Rule

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

= \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

\frac{d}{d x} (x^{4} + 3 x^{3} - x^{2})

\frac{s + 1}{( s ^{2} - 4 s ) ( s + 5 )}

x \to 2 lim (ln (x^{2} - 4))

\frac{d}{d x} (\frac{e ^{x}}{x \cdot cos ( x )})

f^{^{''}} + 16 f = sin (2 x)

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