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One tough integral

  1. Nov 4, 2014 #1
    I would like to know the following indefinite integral:

    (INTEGRAL)arcsin(x/c) dx / tan(x). c is a constant.
    This is not homework...I found it in fron of me while trying to make a 3d model of an enveloped worm gear. I can explain to anyone who isn't bored.
    PLEASE tell me there is a solution...I so feel not :(
  2. jcsd
  3. Nov 4, 2014 #2


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    Science Advisor

    Hey Gmen.

    I guess you should probably ask whether you need it in a closed form using elementary, trig, and transcendental functions or whether you could do something like say a series expansion (like a Taylor series) and integrate it term by term.

    You can use this and depending on how much error you can tolerate just find the cut-off term and compute all terms till that term.
  4. Nov 5, 2014 #3
    This was a really helpful idea. Differentiating is always easier (and possible!) than integrating, and it becomes just a matter of loveable polynomial integration! Thanks! I shall remember this in difficult integrals to come.
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