Integral log{(1/x)-1} from zero to one?????????????????

I= int \int_{0}^{1}log((1-x)/x)) (eq.1)
I= int \int_{0}^{1}log(x/(1-x)) {Since int_{0}^{a} f(x)dx= int_{0}^{a} f(a-x)dx}
I= int \int_{0}^{1} -log((1-x)/x))  (eq.2)
Adding eq.1& eq.2
2I=0
Therefore I=0