This paper focuses on the bandwidth selection in the kernel density estimation in the univariate case. We compared via simulation between the optimal bandwidth selection based on the mean integrated squared error (MISE) and based on the asymptotic mean integrated squared error (AMISE) for various densities and sample sizes. Also, we compared between the MISE and the AMISE in the kernel density estimation. Through simulation, these optimal bandwidths are compared with the bandwidth selection using the methods least squared cross-validation (LSCV), biased cross-validation (BCV), and direct plug-in (DPI).