∫∫f(x,y)dxdy
=∫(a,b)dx∫(c,d)xye^(x^2+y^2)+1dy
=∫(a,b)dx[d-c+x/2*∫(c,d)e^(x^2+y^2)d(x^2+y^2)]
=∫(a,b)dx[d-c+x/2*e^(x^2+y^2)|(c,d)]
=∫(a,b)[d-c+x/2*[e^(x^2+d^2)-e^(x^2+c^2)]dx
=(d-c)(b-a)+∫(a,b)x/2*e^(x^2+d^2)dx-∫(a,b)x/2*e^(x^2+c^2)dx
=(d-c)(b-a)+1/4*[e^(x^2+d^2)-e^(x^2+c^2)]|(a,b)
=(d-c)(b-a)+1/4*[e^(b^2+d^2-e^(b^2+c^2)-e^(a^2+d^2)+e^(a^2+c^2)]