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The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity.
"Derivation of Logarithmic and Logarithmic Hyperbolic Tangent Integrals Expressed in Terms of Special Functions". Mathematics. 8 (687): 687. doi: 10.3390/math8050687. Reynolds, Robert; Stauffer, Allan (2019). "A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function". Mathematics. 7 (1148): 1148. doi: 10.3390 ...
A. Dieckmann, Table of Integrals (Elliptic Functions, Square Roots, Inverse Tangents and More Exotic Functions): Indefinite Integrals Definite 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.
Plot of the logarithmic integral function li(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D. In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number theoretic significance.
The polylogarithm function is equivalent to the Hurwitz zeta function — either function can be expressed in terms of the other — and both functions are special cases of the Lerch transcendent. Polylogarithms should not be confused with polylogarithmic functions , nor with the offset logarithmic integral Li( z ) , which has the same notation ...
Indefinite integrals are antiderivative functions. A constant (the constant of integration) may be added to the right hand side of any of these formulas, but has been suppressed here in the interest of brevity.
Liouvillian functions can be recursively defined as integrals of other Liouvillian functions. More explicitly, a Liouvillian function is a function of one variable which is the composition of a finite number of arithmetic operations (+, −, ×, ÷) , exponentials , constants , solutions of algebraic equations (a generalization of n th roots ...
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.