According to Green's formula,
Original formula = ∫∫ (d) [e x * cosy+√ (x 2+y 2)+x 2/√ (x 2+y 2)-e x * cosy+√ (x 2+y 2)+.
=∫∫(D) 3√(x^2+y^2)dxdy
Let x=pcosk and y=psink, where 0.
Original formula = ∫ (0, π/2) dk * ∫ (0, 2cosk) 3p 2dp.
=∫(0,π/2)dk*p^3|(0,2cosk)
=∫(0,π/2) 8cos^3kdk
=8∫(0,π/2) ( 1-sin^2k)d(sink)
=8[sink-( 1/3)*sin^3k]|(0,π/2)
= 16/3