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Integration w/ trig sub

  1. Aug 18, 2013 #1
    1. The problem statement, all variables and given/known data

    integral of sqrt(x^2-36)/x)

    2. Relevant equations

    sqrt(x^2-a^2) = asec(u)
    Pythagorean identity

    3. The attempt at a solution
    I used trig sub on the x^2-36 and changed that to x=36sec(u) and dx= 36sec(u)tan(u). I simplified the square root in the numerator using sec^2(u)-1 = tan^2(u). This gave me (6tan(u)/36sec(u))(36sec(u)tan(u)) What trig identities do I need to proceed? Or did I use the wrong kind of trig sub? Any help is greatly appreciated in advance.
     
  2. jcsd
  3. Aug 18, 2013 #2

    tiny-tim

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    hi jhahler! :smile:
    isn't that just tan2 ? :wink:
     
  4. Aug 18, 2013 #3

    rock.freak667

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    In your substitution, 'a' should be 6, not 36. Therefore your dx=6sec(u)tan(u).

    After your change your numbers, and simplify, you will need to use the same trig identity you used in the beginning with tan^2(u).
     
  5. Aug 19, 2013 #4

    vanhees71

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    I don't understand why you do such a complicated substitution. Perhaps I don't understand your notation right. It's way easier to use
    [tex]x=6 \sin u.[/tex]
     
  6. Aug 19, 2013 #5

    tiny-tim

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    sec2 - 1 = tan2

    sin2 - 1 = minus cos2 :wink:
     
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