Trigonometric integral

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Trigonometric integrals are a family of integrals which involve trigonometric functions. A number of the basic trigonometric integrals are discussed at the list of integrals of trigonometric functions.

Sine integral:

<math>{\rm Si}(x) = \int_0^x\frac{\sin t}{t}\,dt</math>

<math>{\rm si}(x) = -\int_x^\infty\frac{\sin t}{t}\,dt = {\rm Si}(x) - \frac{1}{2}\pi</math>

Cosine integral:

<math>{\rm Ci}(x) = \gamma + \ln x + \int_0^x\frac{\cos t-1}{t}\,dt</math>

<math>{\rm Cin}(x) = \int_0^x\frac{1-\cos t}{t}\,dt</math>

<math>{\rm ci}(x) = -\int_x^\infty\frac{\cos t}{t}\,dt</math>

Hyperbolic sine integral:

<math>{\rm Shi}(x) = \int_0^x\frac{\sinh t}{t}\,dt = {\rm shi}(x)</math>

Hyperbolic cosine integral:

<math>{\rm Chi}(x) = \gamma+\ln x + \int_0^x\frac{\cosh t-1}{t}\,dt = {\rm chi}(x)</math>

See also: Euler-Mascheroni constant (<math>\gamma</math>).

References

• Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972. (See Chapter 5)
  • (Section 5.2, Sine and Cosine Integrals)de:Integralkosinus

it:Funzioni integrali trigonometrici pl:Cosinus całkowy pt:Integral trigonométrica