Given I=∫01lnx1−xdxI = \int_0^1 \frac{\ln x}{1-x} dxI=∫011−xlnxdx, show that I=−∑n=1∞1n2I = -\sum_{n=1}^{\infty} \frac{1}{n^2}I=−∑n=1∞n21. What is the value?
−π2/6-\pi^2/6−π2/6
−π2/3-\pi^2/3−π2/3
−π/6-\pi/6−π/6
−1-1−1