Distribution of functionals of Brownian motion with linear drift killed elastically at zero

Brownian motion with linear drift on the positive half-line killed elastically at zero is cosidered. We are interested in a result that allows us to calculate the distributions of the integral functionals with respect to the spatial variable of the local time of such process. The explicit form of the distribution of the supremum with respect to spatial variable of the local time is calculated for Brownian motion with linear drift reflected at zero.