`int sin(sqrt(x))/sqrt(x) dx` Evaluate the indefinite integral.

You need to use the following substitution `sqrt x = u` , such that:

`sqrt x = u=> (dx)/(2sqrt x) = du => (dx)/(sqrt x) = 2du `

`int (sin(sqrt x) dx)/(sqrt x) = 2*int sin u du`

`2*int sin u du = -2cos u + c`

Replacing back  `sqrt x ` for u yields:

`int (sin(sqrt x) dx)/(sqrt x) =-2cos (sqrt x) + c`

Hence, evaluating the indefinite integral, yields `int (sin(sqrt x) dx)/(sqrt x) =-2cos (sqrt x) + c.`