# Integrate cosy/sqrt(a-y).dy

1. Dec 29, 2011

### sharks

The problem statement, all variables and given/known data
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.

2. Dec 29, 2011

### HallsofIvy

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

3. Dec 29, 2011

### sharks

You are correct. My mistake. I solved it.

4. Dec 30, 2011

### LCKurtz

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