What is the integration of log (1-x/x) with limit 0 to 1?

I = integral of log([1/x] – 1) dx ——- (1)

I = integral of log(1/1-x – 1) dx

I = Integral 0 to 1 log(1-[1-x]/[1-x]) dx

I = Integral 0 to 1 log(x / 1-x) dx ——- (2)

Add (1) and (2)

2I = 0

I = 0