Not sure what you mean by 'integrate with' a GIS application. I have two questionnaires that are of use but you can't actually embed them into code, you have to request respondents to go to another URI. Anyway, check them out.
sumi.uxp.ie is for a big app with databases etc.
wammi.uxp.ie is for web sites that are not as computationally intensive
The two URIs I have provided are for Academic Licenses, cost free, supported by the revenue from Commercial Licenses. Please go to those sites and read the information carefully. Good luck and best wishes for your research.