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Homework Help: Help With This Supposedly Easy Integration!

  1. Sep 26, 2010 #1
    The problem statement, all variables and given/known data

    Integrate: [tex] \exp(\sin(t)) / (1 + t^2) [/tex]

    The attempt at a solution
    Ok so I tried substituting u=sin(t) du=cos(t)dt but I end up with (1 + arcsin^2(u)) on the bottom and I don't know how to integrate that.
    I also tried letting t=cos(u) dt=-sin(u)du but then I end up with e^(sin(cos(t)) which I've never seen before!
    If anyone knows how to do this please just give me a hint or the first step to take and I will try to do the rest! Thanks
     
  2. jcsd
  3. Sep 26, 2010 #2

    vela

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    I don't think you can integrate that analytically. Is this integral part of a larger problem?
     
  4. Sep 26, 2010 #3
    Ok well it was a differential equation problem that I reduced to that but here is the initial problem:

    [tex] dy/dt + y\cos(t) = 1/ (1+t^2) [/tex]

    so I got an integrating factor of [tex] e^(sint) [/tex] which led to this integral! Hope this helps maybe I did something wrong in first part.
     
  5. Sep 26, 2010 #4

    vela

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    Hmm, perhaps you're expected to leave the solution in terms of the integral.
     
  6. Sep 26, 2010 #5
    I don't think so since the prof asked to solve it in terms of t explicitly. Maybe she made a mistake in writing the problem if this cannot be solved analytically.
     
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