I know how to calculate indefinite integral of sin x but i'm stuck with sin (x)^(1/2).

To solve the indefinite integral of sin sqrt x, I'll
suggest to change the variable x into t^2, such as:

sin
(sqrt x) = sin sqrt t^2 = sin t

x =
t^2

We'll differentiate both
sides:

dx = 2tdt

We'll
re-write the inetgral:

Int sin (sqrt x) dx = Int 2t*sin t
dt

We'll solve the integral by
parts.

Int udv = u*v - Int v
du

u = 2t => du =
2dt

dv = sin t dt => v = -cos
t

Int 2t*sin t dt = -2t*cos t + 2*Int cos t
dt

Int 2t*sin t dt = -2t*cos t + 2*sin t +
C

The indefinite integral of sin sqrt x
is:

Int sin sqrt x dx = 2sin (sqrt x) -
2*sqrt x*cos (sqrt x) + C