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The main difference between differential and integrated rate laws are that differential rate laws are used to describe a reaction rate as a function of the change in concentration over a time period, whereas integrate rate laws show the initial and actual concentration values after a period of time. For example, the differential law means rate = -d[A]/dt, showing that the change in value needs to be provided to answer the question. For integrated (example when n=1), ln[A] = -kt + ln[A0], so you need to know t and the initial and/or final concentration values.
You use integrated rate laws when you need to find the time or final/initial concentrations. Most problems involve using the integrated rate law; we deal with the differential rate law when we need to find reaction orders, etc.
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