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During active states of the brain neurons process their afferent currents with an effective membrane time constant much shorter than its value at rest. This fact, together with the existence of several synaptic time scales, determines to which aspects of the input the neuron responds best. Here we present a solution to the response of a leaky integrate-and-fire neuron with synaptic filters when long synaptic times are present, and predict the firing rate for all values of the synaptic time constant. We also discuss under which conditions this neuron becomes a coincidence detector.