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Integration [ 1/(c+cos(x)) ] by dx

  1. May 15, 2009 #1
    Hi all

    Can you solve the following integration: -

    Integration [ cos(x)/(c+cos(x)) ] by dx
    where c is a constant

    or that one: -

    Integration [ 1/(c+cos(x)) ] by dx

    if one is solved I will be able to make the other
     
  2. jcsd
  3. May 15, 2009 #2
    Re: Integration

    Greetings:

    If you let u = tan(x/2), then dx = 2*du /(u^2+1), sin(x) = 2u/(u^2+1), cos(x) = (1-u^2)/(1+u^2). If you substitute these values appropriately, each integral should return an inverse trig function.

    Regards,

    Rich B.
     
  4. May 15, 2009 #3
    Re: Integration

    Wow really really amazing

    Unfortunately, there is something puzzling me which is:-
    How did you get the idea of substituting u=tan(x/2)
     
  5. May 15, 2009 #4

    HallsofIvy

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  6. May 15, 2009 #5

    Cyosis

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    Re: Integration

    There is no clear cut method to finding primitives. It's much like puzzling, try something out and remember what works.
     
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