  We considered folded spinning string in AdS_5 x S^5 background dual to the
Tr(D^S Phi^J) operators of N=4 SYM theory. In the limit S,J-> \infty and l=pi
J/\sqrt\lambda\log S fixed we compute the string energy with the 2-loop
accuracy in the worldsheet coupling \sqrt\lambda from the asymptotical Bethe
ansatz. In the limit l-> 0 the result is finite due to the massive cancelations
with terms coming from the conjectured dressing phase. We also managed to
compute all leading logarithm terms l^{2m}\log^n l/\lambda^n/2 to an arbitrary
order in perturbation theory. In particular for m=1 we reproduced results of
Alday and Maldacena computed from a sigma model. The method developed in this
paper could be used for a systematic expansion in 1/\sqrt\lambda and also at
weak coupling.
