work integral on hard field

[ori]

given curve:
x=cost
y=sin(2t)
z=cos(2t)
0<=t<=2pi

vectorian field:
F=(exp(x^3),3z/(y^2+z^2),-3y/(y^2+z^2))

so the ingral SF*dr (on the curve)
at the direction of t from 0 to 2pi is?

if i assign the parametrion to the field i get 12pi from integrals on y and z
but i still need to proove that the integral there:
http://www.physicsforums.com/showthread.php?t=43059
is zero
and i think its impossible..

i think using stocks is impossible because building sutaible surface to the curve is imposible

any other sugestions?