Which one is correct?
- The purpose includes to find out which parameter is the most influential.
- The purpose includes finding out which parameter is the most influential.
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The second is correct. After "includes" we use the gerund.
Both sound a little odd because "purpose" usually refers to a single objective while using the word "includes" implies that there are other parts of the purpose aside from finding out which parameter is most influential.
This sounds like scientific writing. Consider instead
Our objectives include finding out which parameter is the most influential and ...
Or if there is only one purpose, use
The purpose of this exercise is to determine which parameter is the most influential.