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Algebraic manipulation of integral

  1. Apr 10, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]
    \int_0^{\frac{\pi}{2}} \frac{\cos(x)}{1+\sin^2(x)} \ln(1+\cos(x))\ dx
    [/tex]


    3. The attempt at a solution
    Can anyone give me a hint as to what to do?
     
  2. jcsd
  3. Apr 14, 2009 #2

    Cyosis

    User Avatar
    Homework Helper

    Re: integral

    Using y=sin(x) followed by partial integration and some algebraic manipulation you can get to the following integral:

    [tex]\int_0^1 \frac{\arctan(y)}{y\sqrt{1-y^2}}\ dy - \int_0^1 \frac{\arctan{y}}{y}\ dy [/tex]

    You know the first integral from a previous question you asked and the second integral is equal to Catalan's constant.
     
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