Integrate$\displaystyle \frac{\ln\left({x^{2}+y^{2}}\right)}{x^{2}+y^{2}}$over the region between the circles$\displaystyle x^{2}+y^{2}=1$and$\displaystyle x^{2}+y^{2}=e^{2}$.

So the integration itself is fine using the quotient rule, but how do I use the circles to get the limits of integration?