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The integral of x^x ... [That's how to write x to the power x when writing in ASCII] This antiderivative is not an "elementary function", which means it cannot be written in terms of the functions you meet in a calculus class. Presumably the paper of Risch will refer to the theory of integration in finite terms due to Liouville 1835. Classic text on the subject: J. F. Ritt, _Integration in Finite Terms_ (Columbia Univ Pr, 1948) Introductory papers, aimed at undergraduates: A.D. Fitt & G.T.Q. Hoare, "The closed-form integration of arbitrary functions". Mathematical Gazette (1993) 227--236. E. Marchisotto & G. Zakeri, "An invitation to integration in finite terms". College Math. J. 25 (1994) 295--308. A modern text (omitting the algebraic case) M. Bronstein, _Symbolic Integration I: Transcendental Functions_ (Springer-Verlag 1997) Here is an old newsgroup post with some explanations... http://correo.hispavista.com/Redirect/mathforum.org/discuss/sci.math/m/141335/141339 -- G. A. Edgar http://correo.hispavista.com/Redirect/www.math.ohio-state.edu/~edgar/ |
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