The temperature integral cannot be analytically integrated and many simple closed-form expressions have been proposed to use
in the integral methods. This paper first reviews two types of simple approximation expressions for temperature integral in
literature, i.e. the rational approximations and exponential approximations. Then the relationship of the two types of approximations
is revealed by the aid of a new equation concerning the 1st derivative of the temperature integral. It is found that the exponential approximations are essentially one kind of rational
approximations with the form of h(x)=[x/(Ax+k)]. That is, they share the same assumptions that the temperature integral h(x) can be approximated by x/Ax+k). It is also found that only two of the three parameters in the general formula of exponential approximations are needed
to be determined and the other one is a constant in theory. Though both types of the approximations have close relationship,
the integral methods derived from the exponential approximations are recommended in kinetic analysis.