General question: What happens if basic integration rules, substitution, and integration by parts method ALL fail. Now what?

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General question: What happens if basic integration rules, substitution, and integration by parts method ALL fail. Now what?

Mathematics
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Depends. Numerical methods...
then you give up , you could try reimann sums for definite integrals but some functions dont have antiderivatives ( well as elementary functions anyway ) for example e^(x^2))
What is it was an indefinite integral? And how could you tell if some function had no antiderivatives?

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