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Dear Raghav Somani,
You cannot integrate xx .This is because the Antiderivative of x^x is not reducible to any elementary functions -- which is not at all unusual. This is true of MOST functions. Calculus books usually list antiderivatives of a hundred or so rather simple functions, and toward the end of the list the antiderivatives get really bizarre. It does not take much effort to come up with a function which can not be precisely integrated. x^x is one.
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Godfrey Classic Prince
IIT-M
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