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The Mathematica manual says:
NIntegrate symbolically analyzes its input to transform oscillatory and other integrands, subdivide piecewise functions, and select optimal algorithms.
How do I extract the specific value of
Method(and other related options) being used for a particular case? In other words, if the method is set to
Automatic, how do I know which method was actually used for integration for a given case?
Can I achieve better accuracy if I modify the parameters for
NIntegrate? I mean, does the automatic selection work well for a majority of cases (if an integrand is non-problematic)? [from your experience]