Rigorous working out I run over in large chapter (5)
I believe the answer is:
logic
'rigorous working out' is the definition.
(figuring something out)
'i run over in large chapter' is the wordplay.
'run' becomes 'go' (both can mean to function or work).
'over' says the letters should be written backwards.
'in' means one lot of letters goes inside another.
'large' becomes 'L' (eg in clothes sizes).
'chapter' becomes 'c' (abbreviation).
'i'+'go'='igo'
'igo' written backwards gives 'ogi'.
'l'+'c'='lc'
'ogi' inserted within 'lc' is 'LOGIC'.
(Other definitions for logic that I've seen before include "Reasoned thinking" , "Dialectics" , "Science of correct reasoning" , "4-ing" , "Aristotelian theories" .)