We present a detailed QCD analysis of nucleon structure functions xF3(x,Q2), based on Laplace transforms and the Jacobi polynomials approach. The analysis corresponds to the next-to-leading order and next-to-next-to-leading order approximations of perturbative QCD. The Laplace transform technique, as an exact analytical solution, is used for the solution of nonsinglet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at low- and large-x values. The extracted results are used as input to obtain the x and Q2 evolution of xF3(x,Q2) structure functions using the Jacobi polynomials approach. In our work, the values of the typical QCD scale ΛMS¯(nf) and the strong coupling constant αs(MZ2) are determined for four quark flavors (nf=4) as well. A careful estimation of the uncertainties shall be performed using the Hessian method for the valence-quark distributions, originating from the experimental errors. We compare our valence-quark parton distribution functions sets with those of other collaborations, in particular with the CT14, MMHT14, and NNPDF sets, which are contemporary with the present analysis. The obtained results from the analysis are in good agreement with those from the literature.