Who's up to the challenge? 26

Calculus Level 5

\[ \large \int_0^1 \left \{ \dfrac{(-1)^{\big\lfloor \frac1x\big\rfloor }}{x}\right \} \, dx = A + B \ln \left( \dfrac C{\pi} \right) \]

The equation above holds true for positive integers \(A,B,\) and \(C\). Find \(A+B+C\).

Notation: \( \{ \cdot \} \) denotes the fractional part function.


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