Find $\int\_{1}^{2}\frac{x-1}{x^2\sqrt{x^2+(x-1)^2}}$

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I tried to solve it by using the property $\int\_{a}^{b}f(x)dx=\int\_{a}^{b}f(a+b-x)dx$  

Let $I=\int\_{1}^{2}\frac{(x-1)dx}{x^2\sqrt{x^2+(x-1)^2}}$  

$I=\int\_{1}^{2}\frac{(2-x)dx}{(3-x)^2\sqrt{(3-x)^2+(2-x)^2}}$  

But this does not seem to work here.I am stuck.What should i do?