Problem on integral calculus

INtegral of (cotx)/((sinx)^(1/2))

please solve it

Shoe Working

cotx/sinx^1/2=cosx/(sinx)^(3/2)
let sinx=t
cosx=dt
it becomes
dt/(t)^(3/2)= -2(t)^(-1/2)
=-2(sinx)^(-1/2)

First, notice that cot x is just cos / sin

So the integral would be ∫cosxdx/(sinx)^(3/2)

Use u substitution now. u = sin x. So du = cos x dx which is what we want.

So this is ∫1/u^3/2 which is -2/sqrt(u) + C

Now just substitute back in and the answer is -2(sqrt(sinx)) + C