Question

given the vector field F (x(x^2+y^2+z^2)^-3/2 + (2yx^2Z^3+xsinxz))i+(y(x^2+y^2+z^2)^-3/2 -2xy^2z^3)j+(z(x^2+y^2+z^2)^-3/2 - (xe^xy+zsinx))k
compute the outward flux of F across the surface x^2+y^2=6y+7-z^2