Trigonometric Integral

Sine integral:

$\{\backslash rm\; Si\}(x)\; =\; \backslash int\_0^x\backslash frac\{\backslash sin\; t\}\{t\}\backslash ,dt$

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

Cosine integral:

$\{\backslash rm\; Ci\}(x)\; =\; \backslash gamma\; +\; \backslash ln\; x\; +\; \backslash int\_0^x\backslash frac\{\backslash cos\; t-1\}\{t\}\backslash ,dt$

$\{\backslash rm\; Cin\}(x)\; =\; \backslash int\_0^x\backslash frac\{1-\backslash cos\; t\}\{t\}\backslash ,dt$

$\{\backslash rm\; ci\}(x)\; =\; -\backslash int\_x^\backslash infty\backslash frac\{\backslash cos\; t\}\{t\}\backslash ,dt$

Hyperbolic sine integral:

$\{\backslash rm\; Shi\}(x)\; =\; \backslash int\_0^x\backslash frac\{\backslash sinh\; t\}\{t\}\backslash ,dt\; =\; \{\backslash rm\; shi\}(x)$

Hyperbolic cosine integral:

$\{\backslash rm\; Chi\}(x)\; =\; \backslash gamma+\backslash ln\; x\; +\; \backslash int\_0^x\backslash frac\{\backslash cosh\; t-1\}\{t\}\backslash ,dt\; =\; \{\backslash rm\; chi\}(x)$

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