A Beautiful Integral

Calculus Level 4

01ln(1x)xdx\large \displaystyle \int_0^1 \dfrac{\ln (1-x) }{x} \, dx If the integral above can be expressed as ABπC -\dfrac AB \pi^C , where A,BA,B and CC are positive integers with AA, and BB being coprime integers, find A+B+CA+B+C.

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