Yes, the algebra works, but you lose the intuition for what's going on. There's a pattern of factorial terms you see with successive integrations: 1/1, 1/2, 1/

Yes, the algebra works, but you lose the intuition for what's going on. There's a pattern of factorial terms you see with successive integrations: 1/1, 1/2, 1/6, 1/24, 1/n!, Multiplying by 2 changes this to 2, 1, 1/3, 1/12, 2/n!. I view that as a clear loser, not a winner.