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

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[tex]\int \frac{\sin x}{x }dx[/tex]
 
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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):
[tex]\int \frac {sin(x)}{x} dx= Si(x)[/tex]
because that is exactly how Si(x) is defined!
 

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