In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary...
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mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions are Si...
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Error function (redirect from Probability integral)
factor of 2 π {\displaystyle {\frac {2}{\sqrt {\pi }}}} . This nonelementary integral is a sigmoid function that occurs often in probability, statistics...
48 KB (7,340 words) - 13:25, 22 June 2025
Antiderivative (redirect from General integral)
elementary functions. To learn more, see elementary functions and nonelementary integral. There exist many properties and techniques for finding antiderivatives...
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List of mathematical identities List of mathematical series Nonelementary integral – Integrals not expressible in closed-form from elementary functions Symbolic...
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elliptic integral. This "solution" generally does not have many uses because most of the nature of the solution is hidden in the nonelementary integral (nonelementary...
21 KB (2,645 words) - 12:32, 25 June 2025
fractions. Alternative methods exist to compute more complex integrals. Many nonelementary integrals can be expanded in a Taylor series and integrated term...
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proven using the Risch algorithm. other nonelementary integrals, including the Dirichlet integral and elliptic integral. It follows directly from the definition...
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Numerical integration (redirect from Integral approximation)
Integral Trapezoidal rule Romberg's method Tanh-sinh quadrature Nonelementary Integral Weisstein, Eric W. "Cubature". MathWorld. "Earliest Known Uses of...
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elementary functions can be expressed as elementary functions Nonelementary integral – Integrals not expressible in closed-form from elementary functions Picard–Vessiot...
4 KB (405 words) - 22:32, 25 November 2022
cannot themselves be expressed as elementary functions. These are called nonelementary antiderivatives. A standard example of such a function is e − x 2 ,...
10 KB (1,421 words) - 16:19, 10 May 2025
antiderivative and nonelementary integral for more details. A procedure called the Risch algorithm exists that is capable of determining whether the integral of an...
9 KB (1,190 words) - 03:36, 22 February 2025
{6A}{5}}y^{5/3}+C_{0}}}}=t} This is an implicit solution which involves a nonelementary integral. This same method is used to solve the period of a simple pendulum...
11 KB (2,623 words) - 13:24, 19 November 2024
Risch algorithm (category Integral calculus)
expression Incomplete gamma function Lists of integrals Liouville's theorem (differential algebra) Nonelementary integral Symbolic integration Geddes, Czapor &...
15 KB (1,884 words) - 06:22, 26 May 2025
elementary functions can be expressed as elementary functions Nonelementary integral – Integrals not expressible in closed-form from elementary functions Richardson's...
11 KB (1,991 words) - 05:56, 3 June 2025
In 1954, this proof appeared in the book of Akiva and Isaak Yaglom "Nonelementary Problems in an Elementary Exposition". Later, in 1982, it appeared in...
44 KB (8,669 words) - 22:13, 22 June 2025
response-model equations are quite complicated and some involve a nonelementary integral; the exact solutions can be found here. It is shown here, however...
42 KB (6,279 words) - 22:27, 3 June 2025