Sine and Cosine Integral (Si, Ci) Calculator

Enter x to compute the sine integral Si(x) and cosine integral Ci(x) with high precision using series and asymptotic expansions, plus a Si(x) graph.

Input

Enter x to compute the sine integral Si(x) and the cosine integral Ci(x).

Value of x

Any real number. Ci(x) is computed only when x is greater than 0.

Sine integral Si(1)

0.9460830704

Cosine integral Ci(1)

0.3374039229

Input x

Graph of Si(x)

The sine integral is Si(x)=∫_0^x (sin t / t) dt. It is an odd function, so Si(−x)=−Si(x), and for large x it oscillates toward π/2 ≈ 1.5708.
The cosine integral is Ci(x)=γ+ln x+∫_0^x ((cos t−1)/t) dt, where γ is the Euler constant ≈ 0.5772. It is not real for x ≤ 0, so Ci(x) is not computed there.
This tool uses a Maclaurin series for small |x| and an asymptotic expansion of auxiliary functions for large |x|, switching between them automatically.
Displayed values are rounded. If you need exact figures, confirm with enough significant digits.

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