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  2. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    Math Major: A Table of Integrals; O'Brien, Francis J. Jr. "500 Integrals of Elementary and Special Functions". Derived integrals of exponential, logarithmic functions and special functions. Rule-based Integration Precisely defined indefinite integration rules covering a wide class of integrands; Mathar, Richard J. (2012). "Yet another table of ...

  3. Integral - Wikipedia

    en.wikipedia.org/wiki/Integral

    Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [a] the other being differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide ...

  4. List of integrals of hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration. Integrals involving only hyperbolic sine functions ⁡ = ...

  5. List of integrals of rational functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    These reduction formulas can be used for integrands having integer and/or fractional exponents. Special cases of these reductions formulas can be used for integrands of the form ( a + b x n + c x 2 n ) p {\displaystyle \left(a+b\,x^{n}+c\,x^{2n}\right)^{p}} when b 2 − 4 a c = 0 {\displaystyle b^{2}-4\,a\,c=0} by setting m to 0.

  6. Newton–Cotes formulas - Wikipedia

    en.wikipedia.org/wiki/Newton–Cotes_formulas

    It is assumed that the value of a function f defined on [,] is known at + equally spaced points: < < <.There are two classes of Newton–Cotes quadrature: they are called "closed" when = and =, i.e. they use the function values at the interval endpoints, and "open" when > and <, i.e. they do not use the function values at the endpoints.

  7. Integral equation - Wikipedia

    en.wikipedia.org/wiki/Integral_equation

    The Numerical Solution of Integral Equations of the Second Kind. Cambridge Monographs on Applied and Computational Mathematics, 1997. George Arfken and Hans Weber. Mathematical Methods for Physicists. Harcourt/Academic Press, 2000. Harry Bateman (1910) History and Present State of the Theory of Integral Equations, Report of the British Association.

  8. Leibniz integral rule - Wikipedia

    en.wikipedia.org/wiki/Leibniz_integral_rule

    In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form () (,), where < (), < and the integrands are functions dependent on , the derivative of this integral is expressible as (() (,)) = (, ()) (, ()) + () (,) where the partial derivative indicates that inside the integral, only the ...

  9. List of integrals of exponential functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    Toyesh Prakash Sharma, Etisha Sharma, "Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.1-8, 2023.