∫[0,1]∫[0,1]y/(1+x^2+y^2)^(3/2)dxdy
=∫[0,1]dx∫[0,1]y/(1+x^2+y^2)^(3/2)dy
=∫[0,1]dx∫[0,1]1/2(1+x^2+y^2)^(3/2)d(1+x^2+y^2)
=∫[0,1]dx1/2*(-2)(1+x^2+y^2)^(-1/2)[0,1]
∫[0,1]{(1+x^2)^(1/2)-(2+x^2)^(1/2)}dx
=ln(x+(1+x^2)^(1/2)-ln(x/√2+(1+1/2x^2)^(1/2))[0,1]
=ln(1+√2)-ln(1/√2+√3/√2)
=ln(2+√2/1+√3)