Save bash command history to syslog

# Increase history size
export HISTSIZE=5000

# In the commands given below - every time a new prompt is issued , bash history is appended to the file, then it is cleared from the current shell's memory,  and current shell reloads the history from the file.

$ export PROMPT_COMMAND="history -a; history -c; history -r; ${PROMPT_COMMAND}"

Another option is to export bash commands to syslog where the bash logs can be centralized and analyzed on demand.

Add the following snipplet to bashrc.

[root@psj]# vim /etc/bashrc

PROMPT_COMMAND=$(history -a)
typeset -r PROMPT_COMMAND

function log2syslog
{
   declare command
   command=$BASH_COMMAND
   logger -p local1.notice -t bash -i -- "$USER : $PWD : $command"

}
trap log2syslog DEBUG