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Trigonometric Integral

  1. Sep 12, 2010 #1
    1. The problem statement, all variables and given/known data

    I'm trying to integrate the following form:

    [tex]y = \int e^{\sin x} dx[/tex]

    3. The attempt at a solution

    I thought about trying to write something like:

    [tex]y = \int e^{\frac{i}{2}e^{-ix} - \frac{i}{2}e^{ix}} dx[/tex]

    But this seems to lead down the road of trying to integrate the form

    [tex]\int e^{e^x} dx[/tex]

    which seems similarly intractable.

    Is there a way to reduce the expression to something simpler, or are you just left w/ leaving the expression in a form like:

    [tex]y(x) = \int_{x_0}^x e^{\sin t} dt[/tex]
  2. jcsd
  3. Sep 12, 2010 #2


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    Gold Member

  4. Sep 12, 2010 #3
    Yes, I tried Wolfram before posting as well and it came up empty for me too..

    My guess is that the integral:

    [tex]y = \int e^{\sin x + 2x} dx[/tex]

    is just as intractable as the first one, yes?

    Thanks for your help..
  5. Sep 12, 2010 #4


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    Again, since wolframalpha can't find a solution in terms of standard mathematical functions, I doubt that you'll be able to evaluate the indefinite integral.
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