Can this integral be solved using elementary functions?

[DryRun]

Homework Statement
Find
\int\frac{\cos y}{\sqrt(a-y)}\,dy

The attempt at a solution
Let U = cos y and dV = \frac{1}{\sqrt(a-y)}

I get: cosy.-2√(a-y) - 2∫√(a-y).siny.dy

So, again, i use partial integration:
Let U = siny and let dV = [-2(a-y)^(3/2)]/3

I get: siny.[-2(a-y)^(3/2)]/3 + (2/3)∫[(a-y)^(3/2)].cosy.dy

But the cycle is endless. I need to get the answer 2siny.

 

[HallsofIvy]

No, you don't. "2 sin(y)" can't possibly be correct because the derivative of 2 sin y is 2 cos y, not "cos(y)/\sqrt{a- y}".

 

[DryRun]

You are correct. My mistake. I solved it.

 

[LCKurtz]

Homework Statement
Find
\int\frac{\cos y}{\sqrt(a-y)}\,dy

The attempt at a solution
Let U = cos y and dV = \frac{1}{\sqrt(a-y)}

You are correct. My mistake. I solved it.

Not with any "elementary" functions; I don't think so.