Who's up to the challenge? 26

Calculus Level 5

01{(1)1xx}dx=A+Bln(Cπ) \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,A,B, and CC. Find A+B+CA+B+C.

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


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