Proposed problem to Mathematical Reflections

Compute

∫∫_{D} \frac{y\sqrt{x^{2} + y^{2}}}{x^{2}} e^{\sqrt{x^{2}+y^{2}}/2}dx dy

D = {(x − 1)^{2} + y^{2} ≤ 1, y ≥ 0}