Everything about Differential Galois Theory totally explained
In
mathematics, the
antiderivatives of certain
elementary functions can't themselves be expressed as elementary functions. A standard example of such a function is
e−x2, whose antiderivative is (up to constants) the
error function, familiar from
statistics. Other examples include the functions:
In other words, the only functions that have "elementary antiderivatives" (for example antiderivatives living in, at worst, an elementary differential extension of
F) are those with this form prescribed by the theorem. Thus, on an intuitive level, the theorem states that the only elementary antiderivatives are the "simple" functions plus a finite number of logarithms of "simple" functions.
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