How Is the Integral of $\frac{\sin x}{x}$ Related to the Sine Integral Function?

[natanael]

\int \frac{\sin x}{x }dx

 

[HallsofIvy]

That anti-derivative cannot be written in terms of elementary functions. It can be written easily in terms of the "sine integral" function, Si(x):
\int \frac {sin(x)}{x} dx= Si(x)
because that is exactly how Si(x) is defined!