Quasilinear elliptic equations of Leary-Lions type with the right hand side in \(L^{1}\) are considered. Two theorems on the existence of unbounded renormalized nonnegative solutions and their comparisons with a nonnegative supersolution are given. The existence of a nonnegative supersolution is assumed in the following two cases: in the first one, the existence of a supersolution of the symmetrized problem, and in the second one, the existence of a renormalized supersolution of the main problem. In order to prove the main results, the following three different methods are well combined and reproduced: the truncation method, the method of Schwarz symmetrization and the sub-super solution method [see L. Boccardo, F. Murat and J. P. Puel, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 11, 213-235 (1984; Zbl 0557.35051)].