  We present a simple derivation of the integral fluctuation theorems for
excess housekeeping heat for an underdamped Langevin system, without using the
concept of dual dynamics. In conformity with the earlier results, we find that
the fluctuation theorem for housekeeping heat holds when the steady state
distributions are symmetric in velocity, whereas there is no such requirement
for the excess heat. We first prove the integral fluctuation theorem for the
excess heat, and then show that it naturally leads to the integral fluctuation
theorem for housekeeping heat. We also derive the modified detailed fluctuation
theorems for the excess and housekeeping heats.
