## Integration in finite terms: Liouville's theory of elementary methods |

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### Contents

Elementary Functions of One Variable | 3 |

Integration of Transcendental Functions | 40 |

Further Questions on the Elementary Functions | 53 |

Copyright | |

5 other sections not shown

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### Common terms and phrases

alge algebraic combination algebraic differential equations algebraic extension algebraic function algebraic relation algebraic solution analytic continuation analytic function assume braic branch point called a monomial Chapter complete monomial consider countable set ct(x curve derivative differential field distinct from zero element elementary functions exists expansion exponent exponential sums expression finite number finite terms fluent follows fractional powers func function of order g is algebraic given holds identically identically zero identity in 9 integration in finite involving irreducible lemma Let 9 Liouville function Liouville's logarithm logarithmic derivative monomials of order Mordukhai-Boltovskoi n-1)-monomials n-logarithm n-monomials neighborhood obtained order less order n-1 order zero pole proof prove question rational combinations rational function regular structure replace 9 residues Riemann surface satisfy an equation second member singularities Suppose theorem theory tion uncountable set vanish identically variable write x-order