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Math Help - How to prove that a function has no closed-form integral?

  1. #1
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    How to prove that a function has no closed-form integral?

    We know from calculus books that some functions (such as e^(-x^2) and sinx/x) have no closed-form integrals but no proofs are given. I want to know where can I find proofs of such statements? Thanks.
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  2. #2
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    Re: How to prove that a function has no closed-form integral?

    such proofs usually use ideas well beyond the scope of calculus texts. for example:

    http://modular.math.washington.edu/e...20b/Conrad.pdf

    one common reference given for such proofs (and indeed, quoted in the link above) is: M. Rosenlicht, Integration in finite terms, American Math. Monthly 79 (1972), 963-972.

    don't feel daunted if either of these is beyond what you have learned so far. it turns out that "integration in elementary terms" is not an elementary subject.
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  3. #3
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    Re: How to prove that a function has no closed-form integral?

    Thank you for the information.
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