Geodesic
So Far, the ``Indefinite Integral''
Matematičeskoe obrazovanie, Tome 104 (2022) no. 4, pp. 28-38.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MO_2022_104_4_a4,
     author = {E. M. Vorobiev},
     title = {So {Far,} the {``Indefinite} {Integral''}},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {28--38},
     publisher = {mathdoc},
     volume = {104},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2022_104_4_a4/}
}
TY  - JOUR
AU  - E. M. Vorobiev
TI  - So Far, the ``Indefinite Integral''
JO  - Matematičeskoe obrazovanie
PY  - 2022
SP  - 28
EP  - 38
VL  - 104
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MO_2022_104_4_a4/
LA  - ru
ID  - MO_2022_104_4_a4
ER  - 
%0 Journal Article
%A E. M. Vorobiev
%T So Far, the ``Indefinite Integral''
%J Matematičeskoe obrazovanie
%D 2022
%P 28-38
%V 104
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MO_2022_104_4_a4/
%G ru
%F MO_2022_104_4_a4
E. M. Vorobiev. So Far, the ``Indefinite Integral''. Matematičeskoe obrazovanie, Tome 104 (2022) no. 4, pp. 28-38. http://geodesic.mathdoc.fr/item/MO_2022_104_4_a4/

[1] Integral Calculator <ext-link ext-link-type='uri' href='https://www.integral-calculator.com'>https://www.integral-calculator.com</ext-link>

[2] Vychislenie neopredelennogo integrala: onlain kalkulyator <ext-link ext-link-type='uri' href='https://functionx.ru/indefint-calculator.html'>https://functionx.ru/indefint-calculator.html</ext-link>

[3] WolframAlpha Online Integral Calculator <ext-link ext-link-type='uri' href='https://www.wolframalpha.com/calculators/integralcalculator'>https://www.wolframalpha.com/calculators/integralcalculator</ext-link>

[4] Karta slov i vyrazhenii russkogo yazyka <ext-link ext-link-type='uri' href='https://kartaslov.ru/%D0%BA%D0%B0%D1%80%D1%82%D0%B0-%D1%81%D0%BB%D0%BE%D0%B2%D0%B0/%D1%82%D0%BE%D0%BB%D0%BA%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5/%D0%BD%D0%B5%D0%BE%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D1%91%D0%BD%D0%BD%D1%8B%D0%B9'>https://kartaslov.ru/tezaurus/neopredelennyi</ext-link>

[5] V. A. Zorich, Matematicheskii analiz, v. 1, MTsNMO, M., 2012, 710 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=751413'>751413</ext-link>

[6] V. A. Ilin, V. A. Sadovnichii, Bl. Kh. Sendov, Matematicheskii analiz, Izd-vo Moskovskogo universiteta, M., 1985, 600 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=836134'>836134</ext-link>

[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. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=830425'>830425</ext-link>

[9] A. M. Ter-Krikorov, M. I. Shabunin, Kurs matematicheskogo analiza, Fizmatlit, M., 2001, 672 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=981188'>981188</ext-link>

[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 <ext-link ext-link-type='uri' href='https://mathportal.org/calculators/calculus/integral-calculator.php'>https://mathportal.org/calculators/calculus/integral-calculator.php</ext-link>

[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: <ext-link ext-link-type='uri' href='https://arxiv.org/abs/1608.04997'>1608.04997</ext-link>