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Very difficult integral to solve

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data
    hey there guys, today I encountered a very difficult integral to solve, at least for me.
    [itex]\int^\sqrt{3}_1 \frac{dx}{\sqrt{(1+x^2)^3}}[/itex]


    2. Relevant equations



    3. The attempt at a solution
    I've tried to substitute but didn't give results. Any suggestions please :)
     
  2. jcsd
  3. Apr 10, 2012 #2

    Dick

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    What substitution did you try? I'd recommend a trig substitution, like x=tan(t).
     
  4. Apr 10, 2012 #3
    Hmmm, alright I'm trying it now.
     
  5. Apr 10, 2012 #4
    I'm now stuck at this point:

    [itex]\int^\frac{\pi}{3}_\frac{\pi}{4} \frac{dt}{cos^3(t)}[/itex]
     
  6. Apr 10, 2012 #5

    Dick

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    You'll need to show how you got there. That's not right and I can't guess what you did.
     
  7. Apr 10, 2012 #6
    x = tan(t)
    dx = d(tan[t]) = [itex]\frac{dt}{cos^2(t)}[/itex]
    x = 1 => tan(t) = 1 => t = [itex]\frac{\pi}{4}[/itex]
    x = [itex]\sqrt{3}[/itex] => tan(t) = [itex]\sqrt{3}[/itex] => t = [itex]\frac{\pi}{3}[/itex]

    so the integral becomes
    [itex]\int^\frac{\pi}{3}_\frac{\pi}{4} \frac{dt}{cos^2(t)\sqrt{(1+tan^2(t))^3}}[/itex]

    oh and now I spot my mistake. It will become cos(t)dt, right?
     
  8. Apr 10, 2012 #7

    Dick

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    Yes it will.
     
  9. Apr 10, 2012 #8
    Ok, thanks for helping me :D
     
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