In article the comparative analysis of differential and integrated consideration of thermodynamic process is carried out. It is shown that use of the rule of replacement of variables of integration leads to a correct conclusion of the main thermodynamic functions (an enthalpy, Helmholtz's function and Gibbs's function). It occurs by integrated consideration of thermodynamic process when parameters change in final (limited) intervals. It is established that Integrated consideration of the law of energy conservation in a general view for the moving final volume of liquid or gas leads to "expanded" option of a formula for the first law of thermodynamics. Thus  the equations register in a differential form taking into account different types of technical work. Communications between the work of pushing through of some volume of gas and work connected with pressure at expansion of volume of gas are shown.