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What (who) is integral cosine - definition
SPECIAL FUNCTION DEFINED BY AN INTEGRAL
Sine integral; Cosine integral; Trigonometric integrals; Hyperbolic sine integral; Hyperbolic cosine integral; Nielsen's spiral; Integral sine; Sin integral; Cos integral; Si(x); Ci(x); Cin(x); Shi(x); Chi(x); Shi function; Sinhc integral; Chi function; Si function
 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg?width=200)
![Integral sine in the complex plane, plotted with a variant of [[domain coloring]].](https://commons.wikimedia.org/wiki/Special:FilePath/Integral sine in the complex plain.svg?width=200 "Integral sine in the complex plane, plotted with a variant of [[domain coloring]].")
 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg?width=200 "Plot of the cosine integral function Ci(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D")
 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg?width=200 "Plot of the hyperbolic cosine integral function Chi(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D")
Henstock–Kurzweil integral
GENERALIZATION OF THE RIEMANN INTEGRAL
Henstock-Kurzweil Integral; Perron integral; Gauge integral; Henstock integral; Denjoy Integral; Henstock-Kurzweil-Stieltjes integral; Perron Integral; Henstock-Kurzweil-Stieltjes Integral; Generalized Riemann integral; Denjoy-Perron integral; Henstock-Kurzweil integral; H-K integral
In mathematics, the Henstock–Kurzweil integral or generalized Riemann integral or gauge integral – also known as the (narrow) Denjoy integral (pronounced ), Luzin integral or Perron integral, but not to be confused with the more general wide Denjoy integral – is one of a number of inequivalent definitions of the integral of a function. It is a generalization of the Riemann integral, and in some situations is more general than the Lebesgue integral.
Pettis integral
Weak integral; Gelfand-Pettis integral; Gelfand–Pettis integral; Gelfand integral; Dunford integral
In mathematics, the Pettis integral or Gelfand–Pettis integral, named after Israel M. Gelfand and Billy James Pettis, extends the definition of the Lebesgue integral to vector-valued functions on a measure space, by exploiting duality.
Improper integral
![The improper integral<br/><math>\int_{-1}^{1} \frac{dx}{\sqrt[3]{x^2}} = 6</math><br/> converges, since both left and right limits exist, though the integrand is unbounded near an interior point.](https://commons.wikimedia.org/wiki/Special:FilePath/Improper integral unbounded internally.svg?width=200 "The improper integral<br/><math>\int_{-1}^{1} \frac{dx}{\sqrt[3]{x^2}} = 6</math><br/> converges, since both left and right limits exist, though the integrand is unbounded near an interior point.")
![An improper Riemann integral of the second kind. The integral may fail to exist because of a [[vertical asymptote]] in the function.](https://commons.wikimedia.org/wiki/Special:FilePath/Improperintegral1.png?width=200 "An improper Riemann integral of the second kind. The integral may fail to exist because of a [[vertical asymptote]] in the function.")
LIMIT OF A DEFINITE INTEGRAL WITH AS ONE OR BOTH LIMITS APPROACH INFINITY OR VALUES AT WHICH THE INTEGRAND IS UNDEFINED
Improper Riemann integral; Improper integrals; Improper Integrals; Proper integral
In mathematical analysis, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number or positive or negative infinity; or in some instances as both endpoints approach limits. Such an integral is often written symbolically just like a standard definite integral, in some cases with infinity as a limit of integration.
Wikipedia
Trigonometric integral
 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg?width=120)
In mathematics, trigonometric integrals are a family of integrals involving trigonometric functions.
