Trigonometric integral

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:

${\rm Si}(x) = \int_0^x\frac{\sin t}{t}\,dt$

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

Cosine integral:

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

${\rm Cin}(x) = \int_0^x\frac{1-\cos t}{t}\,dt$

${\rm ci}(x) = -\int_x^\infty\frac{\cos t}{t}\,dt$

${\rm Shi}(x) = \int_0^x\frac{\sinh t}{t}\,dt = {\rm shi}(x)$

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

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