Trigonometric integral

For simple integrals of trigonometric functions, see List of integrals of trigonometric functions.
Plot of the hyperbolic sine integral function Shi(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D
Plot of the hyperbolic sine integral function Shi(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D

Si(x) (blue) and Ci(x) (green) plotted on the same plot.
Integral sine in the complex plane, plotted with a variant of domain coloring.
Integral cosine in the complex plane. Note the branch cut along the negative real axis.

In mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions.