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Integration question , Help

  1. Dec 24, 2011 #1
    1. The problem statement, all variables and given/known data
    Determine the integral of the following

    ∫(1/(1+cos(x)).dx
    ∫(x+sin(x))/(1+cos(x)).dx

    3. The attempt at a solution

    I tried integration by parts and substution , but didn't work !
    Help :/ !
     
  2. jcsd
  3. Dec 24, 2011 #2
    Show us what you've got. Here are hints:
    1 - Use the identity that cos(x)=2*cos(x/2)-1, and then use a simple substitution.
    2 - Somewhat similar to the first one.
     
  4. Dec 24, 2011 #3
    I got tan(x/2) + C for the first But nothin for the second .
    i did as follows

    ∫(x+sin(x))/(x+cos(x)).dx

    simplified it to

    ∫(x*sec^2(x)).dx + 2∫tan(x/2).dx

    I then i integrated them , i used integration by parts for then right hand integral
    Then i finally got
    2x*tan(x/2)

    Is it correct :D ?
     
  5. Dec 24, 2011 #4

    SammyS

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    That identity should be
    cos(x)=2*cos2(x/2)-1 .​
     
  6. Dec 24, 2011 #5

    SammyS

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    The ∫(x*sec^2(x)).dx + 2∫tan(x/2).dx that you have should be: ∫(x*sec^2(x/2)).dx + 2∫tan(x/2).dx .

    Yes, your answer is correct, if you add an arbitrary constant.
     
  7. Dec 25, 2011 #6
    Oh ok thanks :D ! i always forget the arbitrary unit lol xD
     
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