Bash has feature to write to syslog, that is useful when served accessed by more then one person.
You need to have bash version 4.1+, in my case CentOS 6.4 and CentOS 7 already have it
Open file /etc/bashrc and paste in the end:

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

Next time when you login and syslog:
$ sudo tail -10 /var/log/messages
Sep 21 20:35:57 my-server bash[28245]: pavel : /home/pavel : PATH=$PATH:$HOME/bin
Sep 21 20:35:57 my-server bash[28246]: pavel : /home/pavel : export PATH
Sep 21 20:36:15 my-server bash[28247]: pavel : /home/pavel : sudo tail -50 /var/log/messages
Sep 21 22:42:01 my-server bash[28273]: pavel : /home/pavel : sudo tail -50 /var/log/messages
Sep 21 22:51:35 my-server bash[28276]: pavel : /home/pavel : sudo nano /etc/bashrc
Sep 21 22:51:48 my-server bash[28304]: pavel : /home/pavel : PATH=$PATH:$HOME/bin
Sep 21 22:51:48 my-server bash[28305]: pavel : /home/pavel : export PATH
Sep 21 22:51:58 my-server bash[28306]: pavel : /home/pavel : sudo tail -f /var/log/messages
Sep 21 22:54:46 my-server bash[28309]: pavel : /home/pavel : sudo nano /etc/bashrc
Sep 21 22:56:04 my-server bash[28312]: pavel : /home/pavel : sudo tail -10 /var/log/messages
That can play nicely with log aggregation services. Though it can't be used for security audit purpose, because it's easy to avoid this logging

来自 https://coderwall.com/p/anphha/save-bash-history-in-syslog-on-centos

export PROMPT_COMMAND='history -a { command=$(history 1 | { read x y;echo $y; } );logger -p local1.notice -t bash -i "user=$USER,ppid=$PPID,from=$SSH_CLIENT,pwd=$PWD,command:$command " }'