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The conservative method of calculating the Boltzmann collision integral for simple gases, gas mixtures and gases with rotational degrees of freedom of molecules is presented. In all cases the common approach based on the projection technique of summing up the contributions in the collision integral is used. The method is applied for solving the Boltzmann kinetic equation for two fundamental rarefied gas flow problems: the heat transfer problem and the problem of shock wave structure. A comparison with experimental and numerical data of other authors is reported. It is shown that the considered numerical method allows one to solve the Boltzmann equation for real gases with high accuracy.