Geodesic
On analytical complexity of antiderivatives
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 6, pp. 694-698

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It is shown that the class of all functions of two variables of finite analytical complexity is not closed under integration. It also follows that the class of all functions of finite analytical complexity in the case of three or more variables is not closed under integration. For the case of three or more variables explicit examples of finite complexity functions with infinite complexity antiderivatives are constructed.
Keywords: analytical complexity, integration, finite complexity functions. 
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     author = {Maria A. Stepanova},
     title = {On analytical complexity of antiderivatives},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     publisher = {mathdoc},
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     number = {6},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a4/}
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Maria A. Stepanova. On analytical complexity of antiderivatives. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 6, pp. 694-698. http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a4/