A function f(x)f(x)f(x) is defined by the integral f(x)=∫xexln(t) dtf(x) = \int_{x}^{e^x} \ln(t) \, dtf(x)=∫xexln(t)dt. What is the expression for f′(x)f'(x)f′(x)?
exln(ex)−ln(x)e^x \ln(e^x) - \ln(x)exln(ex)−ln(x)
exln(ex)−xe^x \ln(e^x) - xexln(ex)−x
ex+1−ln(x)e^{x+1} - \ln(x)ex+1−ln(x)
exx−ln(x)e^x x - \ln(x)exx−ln(x)