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Non integrable functions

  1. Dec 20, 2004 #1
    i heard that the function x^x doesnt have any indefinite integral and hence one cant find definite integral by normal methods .. So one has to go for numerical methods , i havent tried this ...
    just curious to know if there exist more fuctions in the same class ...

    mahesh :smile:
  2. jcsd
  3. Dec 20, 2004 #2
    Well, the integral "exists" of course, but it's not the expressible in elementary functions.

    There are many such integrals of this nature.
  4. Dec 20, 2004 #3
    Thanx wolfe, can u tell me where i can find such functions

  5. Dec 20, 2004 #4


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    Yap,just about elliptic integrals.Basically most of the type [itex] \sqrt{P(x)} [/itex],where P(x) is a polynomial with real coeffcients of degree larger of equal with 3,get the "chance" of not having a "cute" antiderivative.Mathematicians invented the famous syntagma "nonelementary function",referring to this sort of functions which come up when searching for antiderivatives.They couldn't come up with a decent definition for this "nonelementary". :tongue2:

    Anyway,when you spot something wrong,i.e.u can't find an antiderivative,try for other tools.Numerical analysis works,but only in the case on definite integral,where the result is a number.Sometimes,u can expand the integrand in Taylor series (though the ray may be small) or express it terms on tabulated "nonelementary functions".The books by Abramowitz & Stegun and Gradsteyn & Rytzhik may turn out to be handy.


    PS.If the antiderivatives exist,but cannot be expressed in terms of "elementary" functions,then the function which makes up the integrand is integrable.
    Last edited: Dec 20, 2004
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