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\begin{equation}  \frac{1}{[A_t]^{n-1}}=\frac{1}{[A_0]^{n-1}}+(n-1)\omega t  \end{equation}  From the integrated rate law, we get the survival function  \begin{equation}  S(t)=\frac{[A_t]}{[A_0]}\sqrt[n-1]{\frac{1}{1+(n-1)\omega t[A_0]^{n-1}}}  \end{equation}  From the survival function, the time dependent rate coefficient is  \begin{equation}  k(t)\equiv(\frac{d\frac{1}{(S(t)^{n-1)}}}{dt})  \end{equation}