How to compute $\iint_{x^2+y^2<1}\int_0^{x^2+y^2} \frac{e^x}{1-z^2}dz dxdy$?
If I change the order of integrating variables, then $=\int_0^1\frac{1}{1-z^2} dz \iint_{z\leq x^2+y^2\leq 1} e^x dxdy$. By changing it into polar coordinate, it seems that we can find its value by usual method. Also, if we use series method, the answer is ugly...How to find its exact value?