SSRS 2012 installation in SharePoint 2013 integration mode , sometimes failed. It may be the due to the SharePoint web applications web.config file may contains
< ! - - comments - - > lines (this is one of the reason for the failure)
Try to remove the comments
< ! - - comments - - > lines lines and try to install.
It’s better to install SSRS in SharePoint 2013 server at initial stage so that before customizing the web.config (with comments lines) to avoid this problem.
Hope this may helpful for someone.