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So Far, the “Indefinite Integral”
Matematičeskoe obrazovanie, no. 4 (2022), pp. 28-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper discusses the mathematical and methodological problems associated with the concept of “indefinite integral” (antiderivative). The importance of including the interval on which the indefinite integral should be calculated in its designation or, at least, in the formulation of tasks for its calculation is substantiated. In the latter, it is also useful to indicate the class of functions to which the antiderivative should belong. This will ensure the uniqueness (up to a constant) of the calculation of antiderivatives. 
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E. M. Vorobiev. So Far, the “Indefinite Integral”. Matematičeskoe obrazovanie, no. 4 (2022), pp. 28-38. http://geodesic.mathdoc.fr/item/MO_2022_4_a4/

[1] Integral Calculator https://www.integral-calculator.com

[2] Vychislenie neopredelennogo integrala: onlain kalkulyator https://functionx.ru/indefint-calculator.html

[3] WolframAlpha Online Integral Calculator https://www.wolframalpha.com/calculators/integralcalculator

[4] Karta slov i vyrazhenii russkogo yazyka https://kartaslov.ru/tezaurus/neopredelennyi

[5] V. A. Zorich, Matematicheskii analiz, v. 1, MTsNMO, M., 2012, 710 pp. | MR

[6] V. A. Ilin, V. A. Sadovnichii, Bl. Kh. Sendov, Matematicheskii analiz, Izd-vo Moskovskogo universiteta, M., 1985, 600 pp. | MR

[7] L. D. Kudryavtsev, Kurs matematicheskogo analiza, Drofa, M., 2003, 703 pp.

[8] Ya. S. Bugrov, S. M. Nikolskii, Vysshaya matematika, v. 2, Drofa, M., 2004, 508 pp. | MR

[9] A. M. Ter-Krikorov, M. I. Shabunin, Kurs matematicheskogo analiza, Fizmatlit, M., 2001, 672 pp. | MR

[10] G. M. Fikhtengolts, Kurs differentsialnogo i integralnogo ischisleniya, v. 2, Fizmatlit, M., 2011, 800 pp.

[11] I. I. Lyashko, A. K. Boyarchuk, Ya. G. Gai, G. P. Golovach, Matematicheskii analiz: vvedenie v analiz, proizvodnaya, integral, Spravochnoe posobie po vysshei matematike, v. 1, Editorial URSS, M., 2001, 360 pp.

[12] I. A. Vinogradova, S. N. Olekhnik, V. A. Sadovnichii, Zadachi i uprazhneniya po matematicheskomu analizu, Posobie dlya universitetov, ped. vuzov, v. 1, Differentsialnoe i integralnoe ischislenie, 3-e izd., ispr., Drofa, M., 2001, 725 pp.

[13] Math Portal https://mathportal.org/calculators/calculus/integral-calculator.php

[14] B. P. Demidovich, Sbornik zadach i uprazhnenii po matematicheskomu analizu, AST, Astrel, M., 2005, 558 pp.

[15] A. V. Begunts, D. V. Goryanin, “Ob aktualnykh podkhodakh k prepodavaniyu temy “Neopredelennyi integral””, Matematika v vysshem obrazovanii, 14 (2016), 7–14

[16] B.M.R. Dos Santos, Ideas for the best teaching integrals: we are teaching wrongly and how to do this right, arXiv: 1608.04997