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We consider the irreversible elementary reaction types  \begin{equation}  A^i \to \mathrm{products}\quad\quad\textrm{for}\quad i=1,2,3,\ldots,n i=1,2,3,\ldots,n.  \end{equation}  The mass-action rate laws for these kinetic schemes are  \begin{equation}  \frac{dC_{A^i}(t)}{dt} = k_iC_{A^i}(t)\quad\quad\textrm{for}\quad i=1,2,3,\ldots,n i=1,2,3,\ldots,n.  \end{equation}  Experimentalists deduce rate laws from data that is the integrated rate law. For the $i^{th}$-order reaction the integrated rate law is  \begin{equation}