bash history log all commands to syslog

.bash_profile

#log all your bash command to syslog
function log2syslog
{
   declare COMMAND
   COMMAND=$(fc -ln -0)
   logger -p local1.notice -t bash -i -- "${USER}:${COMMAND}"
}
trap log2syslog DEBUG

#moredetails can be found here
#http://mywiki.wooledge.org/BashFAQ/077

.bashrc

PROMPT_COMMAND='history -a >(tee -a ~/.bash_history | logger -t "$USER[$$] $SSH_CONNECTION")'