$\displaystyle
x=\sqrt{2}\cos t\\
$
$\displaystyle
y=\sqrt{2}\sin t \\
$
$\displaystyle
z=\frac{4t}{\pi}\\
$
$\displaystyle
A=\int^{(1,1,1)}_{(0,0,0)}\frac{yz}{1+x^2y^2z^2}dx +\frac{xz}{1+x^2y^2z^2}dy+\frac{xy}{1+x^2y^2z^2}dz \\
$
$\displaystyle
A=\int^{(1)}_{(0)}\frac{\sqrt{2}\sin tz}{1+(\sqrt{2}\cos t)^2(\sqrt{2}\sin t)^2z^2}(dx)+\frac{xz}{1+x^2(\sqrt{2}\sin t)^2z^2}0+
$
$\displaystyle
+\frac{xy}{1+x^2(\sqrt{2}\sin t)^2z^2}0
$
i dont know if i am doing it the right way
becausei got a very complexed expression and this only one third