Saw this referred to in A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity and it made me shudder – as I always seemed to struggle with it at ‘A’ level maths – so here, for my own benefit, is a quick proof/explanation of the method.
The general rule is:
And why is this so?
From the product rule we know:
And, integrate both sides and we have:
Of course, we still have to apply this sensibly to make our problem easier to integrate!