What is the antiderivative of the function lnx/square root x?

To determine the antiderivative of the given function,
we'll have to calculate the indefinite integral of the given
function:

`int` ln x
dx/`sqrt(x)`

We'll integrate by parts using the
formula:

`int` udv = uv - `int`
vdu

Let u = ln x => du =
dx/x

Let dv = dx/`sqrt(x)` => v =
2`sqrt(x)`

`int` ln xdx/`sqrt(x)` = 2ln x*`sqrt(x)` - `int`
2`sqrt(x)` dx/x

`int` ln xdx/` ` `sqrt(x)` =
ln(x^2)*`sqrt(x)` - 2x^(-1/2 + 1)/(1 - 1/2) + C

`int` ln x
dx/`sqrt(x)` = ln(x^2)*`sqrt(x)` - 4 `sqrt(x)` + C

`int` ln
x dx/`sqrt(x)` = `sqrt(x)` [ln (x^2) - 4] +
C

The antiderivative of the function is Y =
`sqrt(x)` [ln (x^2) - 4] + C