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