When I was preparing for the UK STEP examinations, one of the questions had you evaluate an integral I by carefully choosing another integral J such that I+J an

When I was preparing for the UK STEP examinations, one of the questions had you evaluate an integral I by carefully choosing another integral J such that I+J and I-J were both very easy to evaluate. From there it's just a matter of simultaneous equations. I've never seen this trick replicated elsewhere in research or teaching, but it's stuck with me as an incredibly elegant method.