In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary...

mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions are Si...

factor of 2 π {\displaystyle {\frac {2}{\sqrt {\pi }}}} . This nonelementary integral is a sigmoid function that occurs often in probability, statistics...

elementary functions. To learn more, see elementary functions and nonelementary integral. There exist many properties and techniques for finding antiderivatives...

List of mathematical identities List of mathematical series Nonelementary integral – Integrals not expressible in closed-form from elementary functions Symbolic...

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...

fractions. Alternative methods exist to compute more complex integrals. Many nonelementary integrals can be expanded in a Taylor series and integrated term...

proven using the Risch algorithm. other nonelementary integrals, including the Dirichlet integral and elliptic integral. It follows directly from the definition...

Integral Trapezoidal rule Romberg's method Tanh-sinh quadrature Nonelementary Integral Weisstein, Eric W. "Cubature". MathWorld. "Earliest Known Uses of...

elementary functions can be expressed as elementary functions Nonelementary integral – Integrals not expressible in closed-form from elementary functions Picard–Vessiot...

antiderivative and nonelementary integral for more details. A procedure called the Risch algorithm exists that is capable of determining whether the integral of an...

cannot themselves be expressed as elementary functions. These are called nonelementary antiderivatives. A standard example of such a function is e − x 2 ,...

{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...

expression Incomplete gamma function Lists of integrals Liouville's theorem (differential algebra) Nonelementary integral Symbolic integration Geddes, Czapor &...

elementary functions can be expressed as elementary functions Nonelementary integral – Integrals not expressible in closed-form from elementary functions Richardson's...

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...

response-model equations are quite complicated and some involve a nonelementary integral; the exact solutions can be found here. It is shown here, however...