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On Indefinite Integrals Which Contain Algebraic Functions

In: Cauchy's Calcul Infinitésimal

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  • Dennis M. Cates

Abstract

We call algebraic functions those that we form by only employing the first operations of the algebra, namely, addition, subtraction, multiplication, division, and the raising of variables to fixed powers. The algebraic functions of one variable are rational when they contain only integer powers of this variable, that is to say, when they are reduced to entire functions or to rational fractions. They are irrational otherwise.

Suggested Citation

  • Dennis M. Cates, 2019. "On Indefinite Integrals Which Contain Algebraic Functions," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 149-154, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-11036-9_28
    DOI: 10.1007/978-3-030-11036-9_28
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