# Integrate (1-a-cos x)-1/2

1. Jul 19, 2011

### c299792458

1. The problem statement, all variables and given/known data
how does one integrate (1-a-cos x)-1/2, where a is an arbitrary constant?

2. Relevant equations
as above

3. The attempt at a solution
Thought of writing cos x as 1-2*(sin($\frac{x}{2}$))2
then the integrand simplifies to [2*(sin($\frac{x}{2}$))2 - a]-1/2...
But then...? Is there a more elegant way of integrating this?

2. Jul 19, 2011

### Dickfore

3. Jul 20, 2011

### Ray Vickson

Re: Integration

It is a non-elementary integral. Maple 9.5 gets:
J:=int(1/sqrt(b-cos(x)),x):simplify(J,symbolic);

- 2*EllipticF(cos(x/2),sqrt(2/(b+1)) )/sqrt(b+1),

where EllipticF is the incomplete elliptic integral of the first kind.

RGV