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A theoretical and experimental study of the optical gain and the linewidth enhancement factor (LEF) of a type-I quantum-cascade (QC) laser is reported. QC lasers have a symmetrical gain spectrum because the optical transition occurs between conduction subbands. According to the Kramers-Kronig relation, a zero LEF is predicted at the gain peak, but there has been no experimental observation of a zero LEF. There are other mechanisms that affect the LEF such as device self-heating, and the refractive index change due to other transition states not involved in lasing action. In this paper, the effects of these mechanisms on the LEF of a type-I QC laser are investigated theoretically and experimentally. The optical gain spectrum and the LEF are measured using the Hakki-Paoli method. Device self-heating on the wavelength shift in the Fabry-Perot modes is isolated by measuring the shift of the lasing wavelength above the threshold current. The band structure of a QC laser is calculated by solving the Schrödinger-Poisson equation self-consistently. We use the Gaussian lineshape function for gain change and the confluent hypergeometric function of the first kind for refractive index change, which satisfies the Kramers-Kronig relation. The refractive index change caused by various transition states is calculated by the theoretical model of a type-I QC laser. The calculated LEF shows good agreement with the experimental measurement.