  In this paper we derive the Laplace transforms of the integral functionals $$
\int_0^\infty (p(\exp(B^{(\mu)}_t)+1)^{-1}+ q(\exp(B^{(\mu)}_t)+1)^{-2}) dt, $$
$$ \int_0^\infty (p(\exp(R^{(3)}_t)-1)^{-1}+ q(\exp(R^{(3)}_t)-1)^{-2}) dt, $$
where $p$ and $q$ are real numbers, $\{B^{(\mu)}_t: t\geq 0\}$ is a Brownian
motion with drift $\mu>0,$ BM($\mu$), and $\{R^{(3)}_t: t\geq 0\}$ is a
3-dimensional Bessel process, BES(3). The transforms are given in terms of
Gauss' hypergeometric functions and it is seen that the results are closely
related to some functionals of Jacobi diffusions. This work generalizes and
completes some results of Donati--Martin and Yor and Salminen and Yor.
