In this paper, we discuss the propagation of optical pulses in the nonlinear optical fibers. The generalized higher-order nonlinear Schrödinger equation (NLSE) is under consideration as a governing model. The studied model is composed of group-velocity dispersion, self-phase modulation, third-order dispersion, self-steepening and stimulated Raman scattering. Researchers have been studying a wide range of natural phenomena in depth, and nonlinear science has gradually become a part of people’s consciousness. We have extracted the optical pulses in different forms like bright, dark, singular and combined solitons by assistance of recently developed integration tool, namely the new extended direct algebraic method (NEDAM). Moreover, the solutions for the hyperbolic, periodic and trigonometric functions are retrieved. Using proper parameters in numerical simulations and physical explanations, it is possible to demonstrate the importance of the findings. It is proposed that the offered method can be utilized to support nonlinear dynamical models applicable to a wide variety of physical situations. We hope that a wide spectrum of engineering model professionals will find this study to be beneficial.