dx 6 a Consider the integral I = x log x log x to simplify this integral. i Use the substitution u = ii Determine the integral for u and then back-substitute to find the original integral. b In studying the survival of a population after an epidemic, Gompertz proposed the following alternative differential equation for population growth dN = kN log N, dt where N is the population at time t. Use the results of part a to solve this differential equation.