I need to use NIntegrate to obtain highly accurate values of some integral. The relative error should be 1.E-16 or smaller. Is this possible? I am not sure how to proceed. NIntegrate has a number of confusing options: AccuracyGoal, PrecisionGoal and WorkingPrecision. I am playing with these, trying to set them to various values, but whatever I do I obtain results which do not seem to have an error smaller than 1.E-7 or so. I would appreciate an advice.