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Ignacio Darnaude Rojas - Marcos Cabeza del Rey Don Pedro , 9 ( 2º B ) 41004 - Sevilla ( Spain ) e-mail : ummo@hispavista.com Página Web (URL /Website ) : http://correo.hispavista.com/Redirect/www.galeon.com/darnaude Dear Sirs , Please first realize this unexpectod request is not a routine petition at all , but an old unresolved soul?problem to the writer , a graduated in Economics and by the way enamoured of Mathematics , his second lifelong love affair. ( He is , too , fallen in love with some imaginable sort of solution to the handsome exponential equation “A elevated to x + B elevated to x = C ” ). ( A ^x + B ^x = C ). I am extremely interested in finding finally, after many years of fruitless search , the rather arcane answer to my personal “Fermat Last Theorem” , I think an easy task for Euler or Galois : the mysterious integral which reads as follows : "Indefinite integral of X elevated to x by differential x" [ Integral X power x dx ][Integral X to the power x dx ] S X ^ x dx In other words I am looking for some elusive antiderivative algebraical function that , derived , result into a beautifully complex and elegant potential?exponential expression : X elevated to x. [ X ^ x ]. Be sure this remote friend Ignacio would be delighted if you wisely make the Sevillian happy by means of forwarding him his keenly wanted explanation of this damned integral , send him the address of possible academic sources of information ( the most prestigious worldwide university departments especialized in Math ) , or specific bibliography dealing with the above mentioned “Integral of X elevetad to x differential x” : S X ^ x dx . [ In respect to the above mentioned integral S X^x dx , I refer to the paper by Robert H.Risch The problem of integration in finite terms ( Transactions of the American Mathematical Society , Vol. 139 , ( 1969 ) , pages 167-189 ) ]. I remain mathematically and of course humanly grateful to you for such an integral informative favour. With my warmest regards |
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