I am struggling to integrate logarithms, and powers of logarithms, along a circular contour about the origin. The way to do this problem is to find the indefinate integral of the logarithm, and then evaluate at z=R e^0 to z=R e^(2 Pi I). However, Mathematica will automatically set e^(2 Pi I) = 1, and then the integral becomes zero. Or it says that Log[R e^(2 Pi I)]=Log[R], instead of Log[R]+2 Pi I. How does one stop it doing this?