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Integrate sin(sinx))

  1. Dec 11, 2011 #1
    What is ∫sin(sin(x)) dx ?

    I was told that it was not an elementary function. Then what function is it?
     
  2. jcsd
  3. Dec 11, 2011 #2

    Dick

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    I don't think it has a name yet. Do you want to name it?
     
  4. Dec 11, 2011 #3
    Haha how can it not be already named? Can't someone solve it?
     
  5. Dec 12, 2011 #4

    SammyS

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    Solve what?

    You've been told that it's not an elementary function.

    About the best that can be done is to express the integrand as a Taylor series, the integrate that.
     
  6. Dec 12, 2011 #5

    Dick

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    Some integrals that can't be expressed as elementary functions are useful enough that they are given special names. E.g. http://en.wikipedia.org/wiki/Exponential_integral Not being able to 'solve' something doesn't it isn't useful or that there is nothing you can say about it.
     
  7. Dec 12, 2011 #6
    ohhh
    But I just downloaded Mathematica, and when I integrate sin(sin(x)), it gives me: (1/2)(sin2(x2))
    But I cant see how taking the derivative of that gives sinsinx
    Is Mathematica wrong then?
     
  8. Dec 12, 2011 #7
    Nvmmm I typed in the sin function in wrong format lol
     
  9. Dec 12, 2011 #8

    dextercioby

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    And even the mighty Mathematica who knows the work of Gradsheyn and Rytzhik by heart couldn't do it...
     
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