Math CentralQuandaries & Queries


Question from ANGIKAR, a student:
what would be the integration of (X^Xdx)?


I very much doubt if it can be expressed in terms of elementary functions. Differentiation tends to keep functions at the same level of complexity or occasionally make them simpler [though perhaps longer]; integration thus keeps on breaking out of finite families of functions and yielding more complicated things.

Thus integrating 1 gives a nonconstant function, while integrating 1/x and 1/(1+x2) yields transcendental functions. Integrating exp(-x2) yields the "error function", and so on.

Good Hunting!


There are sophisticated computer programs to can be used for integration. One of these programs is Mathematica. There is an online version of the Mathematica Integrator. Follow the link and enter x^x.


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