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Another Integral Problem

  1. Feb 9, 2014 #1
    1. The problem statement, all variables and given/known data

    http://i.imgur.com/u1De0i3.png

    2. Relevant equations



    3. The attempt at a solution

    So I notice that the bottom is in the form x^2 - a^2 where a = 7, so I use trig substitution to start this off.

    x = 7secθ, dx = 7secθtanθ, and finally, x^2 - 49 = 49sec(θ)^2 - 49 = 49 tan^2(θ)
    Substituting into the integral, I get
    7∫(sec^2(θ) - secθ) dθ, which basically turns into:
    7tanθ - 7 ln |secθ + tanθ|.
    After putting x back into the equation, I end up with:
    √(x^2-49) - 7 ln|(x/7) + (√(x^2-49)/7)| + C
    I would just like your help in checking my answers, because I don't get any of the answers provided in the multiple choice, and i'm always hesitant to pick "none of the above". Thank you.
     
  2. jcsd
  3. Feb 9, 2014 #2

    Dick

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    One of those answers differs from your answer by a constant.
     
  4. Feb 9, 2014 #3
    What do you mean? Hmm, I can't really see any way to rearrange it like that, I think I know the one you're talking about though.
     
  5. Feb 9, 2014 #4

    Dick

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    For example, log(x/7)=log(x)-log(7).
     
  6. Feb 9, 2014 #5
    Ohhhh! Let's see if I can go any further now, thanks alot.
     
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