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\begin{equation}  \frac{dC_{A^i}(t)}{dt} = k_i(t)C_{A^i}(t).  \end{equation}  Experimentalists deduce rate laws from data that is corresponding to  the integrated rate law. For the $i^{th}$-order reaction the traditional  integrated rate law law, with $k_i(t)\to\omega$  is \begin{equation}  \frac{1}{[C_A(t)]^{i-1}} = \frac{1}{[C_A(0)]^{i-1}}+(i-1)\omega t.  \end{equation}