A lot of apparently innocent elementary functions, like exp(-x^2) or (sin x)/x, have not antiderivatives in terms of elementary functions. I've read that "Differential Galois theory" explains this, and gives an algorithmic method to know if a given elementary function has or has not elementary antiderivative.(adsbygoogle = window.adsbygoogle || []).push({});

Please, can you explain to me the fundamental, core ideas of this theory?. Some practical, as elementary as possible references? Examples of its use?. Thank you, kowalski.

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# Differential Galois Theory: exp(-x^2) has no elementary antiderivative

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