The function Si(x) can be obtained when we integrate $\frac {sin(x)}x$. But how would we go about integrating Si(x)?
More information about the function Si(x) can be found here
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$\begingroup$This can be done analytically. You have$$\DeclareMathOperator{\Si}{Si} \int \Si(x)\,dx = x \Si(x) + \cos(x) + \text{constant} $$Test by differentiating the RHS:$$ \frac{d}{dx} (x \Si(x) + \cos(x) + \text{constant}) = \Si(x) + x \frac{\sin x}{x} - \sin(x) = \Si(x) $$If you couldn't guess the result, you can get it by integrating by parts: $$ \int \Si(x)\,dx =\int 1 \cdot \Si(x)\,dx = x \Si(x) - \int x \frac{\sin x}{x} = x \Si(x) + \cos x + \text{constant} $$
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