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More compact collections can be found in e.g. Brychkov, Marichev, Prudnikov's Tables of Indefinite Integrals, or as chapters in Zwillinger's CRC Standard Mathematical Tables and Formulae or Bronshtein and Semendyayev's Guide Book to Mathematics, Handbook of Mathematics or Users' Guide to Mathematics, and other mathematical handbooks.
The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals . In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration .
In mathematics, the definite integral ()is the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the lines x = a and x = b, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total.
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.
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.
the integral is called an indefinite integral, which represents a class of functions (the antiderivative) whose derivative is the integrand. [19] The fundamental theorem of calculus relates the evaluation of definite integrals to indefinite integrals. There are several extensions of the notation for integrals to encompass integration on ...
The process of finding the value of an integral is called integration. [46]: 508 The indefinite integral, also known as the antiderivative, is the inverse operation to the derivative. [48]: 163–165 F is an indefinite integral of f when f is a derivative of F. (This use of lower- and upper-case letters for a function and its indefinite ...
The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.