Codeigniter applications can be integrated into various content management systems; such as WordPress, Joomla and Expression Engine. Since Expression Engine is built with Codeigniter, it is the best fit. For those who want to integrate a Codeigniter application into WordPress, here are a couple of links.
Integrating Codeigniter into WordPress A
Integrating Codeigniter into WordPress B
Integrating Codeigniter into WordPress C
Dumping Codeigniter inside WordPress
Besides the links the mentioned above, there is an another valid alternative for which using a Codeigniter application inside a WordPress CMS can be achieved. Simply dump a codeigniter installation inside the WordPress installation. For example, if the site was called mysite.com the Codeigniter folder would reside at mysite.com/codeigniter. Now, an external link from, the main menu or from any other link could point to the desired folder. With this solution, the Codeigniter installation could use a stand-alone database or the WordPress database. To use the WordPress database, the current Codeigniter database would need to be dumped into the WordPress database and the config.php file would need to be edited to connect to the new database.
Please hear me out, before you decide to comment regarding why this idea for using Codeigniter inside of WordPress is a bad idea. With Codeigniter, after learning its ways, you will see that its logic to making applications is superior to any content management system; unlike plugins and extensions and modules that are cms specific and take a long time to recode. It is so portable that you can use it anywhere in other content management systems for which the only really extra work is to use the default CMS template. Once you set the link to the existing CMS templates, it will already exist in the cache and never look out of place. You would never know Codeigniter is inside a cms except for looking at the source code. After looking at the source code, it could be anything since there is not trace to a Codeigniter installation. Finally, the Codeigniter app is ready for Expression as it is, or with simple modifications it can be made into a module.
As far as SEO goes, no problem. Since it will link form the menu it will be picked up. The page can also be added to the sitemap.