Consider the following first-order reaction,
A → B
The rate of the chemical reaction is given by the rate law expression as,
Rate,
R = k [A] where [A] is the concentration of the reactant A and k is the velocity constant or specific rate of the reaction.
The instantaneous rate is given by,

If [A0] is the initial concentration of the reactant and [A]t at time t, then by integrating the above equation,

This is the integrated rate equation for the first order reaction. This is also called integrated rate law.