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Integration of (cosx/ (2-cosx))

  1. Dec 29, 2006 #1

    Mo

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    1. The problem statement, all variables and given/known data
    integrate with respect to x


    2. Relevant equations

    integral of cos x / (2 - cos x) dx

    3. The attempt at a solution
    I attempted to use the substitution of tan (x/2) but got lost in it. I dont think it was correct to subsititute t = tan(x/2) because it was not in the correct form. [am i right in thinking to substitute in t=tan(x/2) we need an equation of the form 1 / (a + bsinx + ccosx) ?]

    I also tried dividing top and bottom by cos x but I am unsure if this would lead me anywhere.

    I'm hoping for a little pointer in how to start.

    Thanks.
     
  2. jcsd
  3. Dec 30, 2006 #2

    siddharth

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    Homework Helper
    Gold Member

    (i) The substitution of tan(x/2) is sometimes used when the integrand is a rational function of sin and cos. You might find this link useful.

    (ii) In your problem, try eliminating the cos function from the numerator first. Here's a hint, try adding and subtracting '2' (to the negative of the integrand) in the numerator. Can you take it from here?
     
    Last edited: Dec 30, 2006
  4. Dec 30, 2006 #3

    Mo

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    Thank you very much indeed! I do not think I would have got that in a loooong time! Thanks for the link as well.

    Regards,
    Mo.
     
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