# Non-elementary functions with elementary proofs!

Calculus Level 5

$\large \text{Si}(x) = - \int_{x}^{\infty} \frac{\sin(t)}{t} \, dt \\ \large \text{Ci}(x) = - \int_{x}^{\infty} \frac{\cos(t)}{t} \, dt$

The functions $$\text{Si}(x)$$ and $$\text{Ci}(x)$$ are usually defined as above. Given that

$\large \left| \int_{0}^{\infty} \sin(x) \text{Si}(x) \, dx + \int_{0}^{\infty} \cos(x) \text{Ci}(x) \, dx \right| = \frac{A\pi^{B}}C,$

where $$A,B,C$$ are all positive integers with $$A,C$$ coprime. Find $$A + B + C$$.

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