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Impossible Integration involving cosx/sqrt(a-bcosx)

  1. Jan 22, 2016 #1
    Ok, I have encountered this one a few hours ago:
    [tex]\int \frac{cos x}{\sqrt{a - b cos x}}dx [/tex]
    I have tried all techniques I know, integration by part, half-angle formula, substitution, trigo approach, and so on, but it seems, I could not integrate this one. I am no noob in integration, but this one is a bit difficult. How do I integrate it?
  2. jcsd
  3. Jan 22, 2016 #2
    Wolfram Alpha? Integral table?
  4. Jan 22, 2016 #3
    Mathematica returns the same result found in Gradshteyn and Ryzhik.
  5. Jan 22, 2016 #4
    I suspected that. After I learned that a lot of integrals cannot be solved without essentially defining a new function (like erf and the ellipticals), I got in the habit after spinning my wheels a bit with the standard techniques of looking them up in G&R to see if they were do-able.

    When MMa came along, it was faster than looking in G&R. WA is even more convenient.
  6. Jan 23, 2016 #5
    Yes of course, it is really convenient to look into table of integrals, but it is just impossible to do on exams. I hope we could have a technique to solve it.
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