From Longman Dictionary of Contemporary Englishburn the midnight oilburn the midnight oilinformalWORK HARD to work or study until late at night → burn
Examples from the Corpus
burn the midnight oil• Five worlds split into several sections is certainly enough to keep you burning the midnight oil.• Lawmakers were burning the midnight oil last night, as the debate continued.• Ingrid and other loyal friends spent long hours burning the midnight oil with her when it came to the final typing. 