I'm not sure why you would want to integrate the two, as Wordpress is not a development framework. I am making a BIG assumption that you really want to just have it in the same 'directory' and be able to utilize the same database?
I've seen that done before, and it involves simply sharing config files for your database (include wordpress config inside codeigniter, etc).
Just stick CI inside a folder inside your Wordpress directory:
/website/
/ci/ (codeigniter runs inside here)
/wp-content/
/wp...
...
index.php (wordpress)
.htaccess (combined wordpress / ci functionality)
Then you would just duck inside the /ci
folder for CI functionality and redirect back to Wordpress after.
As far as integrating with merge of CODE (ie, wordpress with CI running inside of it or vice versa) that is pointless and most would argue a waste of time.
Wordpress already offers most of the features you would want to build in CI (session tracking / database active querying / basic CRUD functionality / user management).
If all you seek is to utilize some small 'functions' in Wordpress that you get in CI, I would say focus on porting those alone.
Nothing good can come of you merging two applications together like this.
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