In this article, we give several differentiation and integrability formulas of special and composite functions including trigonometric function, and polynomial function.
@article{bwmeta1.element.doi-10_2478_v10037-010-0016-8,
author = {Bo Li and Na Ma and Xiquan Liang},
title = {Integrability Formulas. Part II},
journal = {Formalized Mathematics},
volume = {18},
year = {2010},
pages = {129-141},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0016-8}
}
Bo Li; Na Ma; Xiquan Liang. Integrability Formulas. Part II. Formalized Mathematics, Tome 18 (2010) pp. 129-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0016-8/
[1] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
[2] Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.
[3] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.
[4] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
[5] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.
[6] Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990.
[7] Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.
[8] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
[9] Jarosław Kotowicz. The limit of a real function at infinity. Formalized Mathematics, 2(1):17-28, 1991.
[10] Xiquan Liang and Bing Xie. Inverse trigonometric functions arctan and arccot. Formalized Mathematics, 16(2):147-158, 2008, doi:10.2478/v10037-008-0021-3.[Crossref]
[11] Konrad Raczkowski. Integer and rational exponents. Formalized Mathematics, 2(1):125-130, 1991.
[12] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.
[13] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
[14] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
[15] Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195-200, 2004.
[16] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
[17] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
[18] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
[19] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.