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Possible three-nucleon forces that may be considered in addition to a widely accepted two-pion exchange three-nucleon force are studied to improve the fit to experimental data of proton-deuteron scattering. Calculations are performed with including effects of long-range Coulomb force by a recently developed method to solve the Faddeev equation in coordinate space. Two different kinds of three-nucleon potentials: a phenomenological potential and one due to the exchange of pion and sigma bosons, are presented and compared with experimental data of elastic differential cross sections, a tensor analyzing power, and a nucleon-to-nucleon polarization transfer coefficient.