Nonlinear integral equations equivalent to the Hubbard model Bethe Ansatz are used to evaluate the highest (i.e. antiferromagnetic) anomalous dimensions of scalar operators in N=4 SYM. In specific, multiloops corrections are computed in the SU(2) operator subspace and compared with BDS Bethe Ansatz predictions. In the general SO(6) case only one loop calculations can be finalised. The method proposed here is quite general and originates in the exact evaluation of finite size corrections to observables of spin chains. It is especially suitable for numerical evaluations and it allows for explicit computation of the leading finite size corrections.