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

  1. Jul 19, 2011 #1
    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([itex]\frac{x}{2}[/itex]))2
    then the integrand simplifies to [2*(sin([itex]\frac{x}{2}[/itex]))2 - a]-1/2...
    But then...? Is there a more elegant way of integrating this?
     
  2. jcsd
  3. Jul 19, 2011 #2
  4. Jul 20, 2011 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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
     
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