TOPIC:

I create more than three learning objectives .but in time of exporting i frequently notice its size .it is 0 KB always .please suggest me to escape this error.and tell me the way how to integrate to atingi lms.

Those are two very different questions.
What platform is your Xerte hosted on? xampp? linux?
The 0kb export is most likely caused by the fact that the zip extension is not enabled for PHP. Try to enable the zip extension.

I don't know Atingi LMS. It seems to be based on Moodle, so you should be able to integrate with LTI (if your Xerte install is reachable over the internet) or SCORM.