Primitive of Sine Integral Function

Theorem

 * $\displaystyle \int \map \Si x \rd x = x \map \Si x + \cos x + C$

where $\Si$ denotes the sine integral function.

Proof
By Derivative of Sine Integral Function, we have:


 * $\displaystyle \frac \d {\d x} \paren {\map \Si x} = \frac {\sin x} x$

So: