# My favourite integral problem

PGvdVeen shared this question 6 years ago

One of my favourite algebraic problems is to integrate the function x^-x between 0 and 1.

There is a wonderfull esthetic answer, given by one of the Bernoulli's ages ago.

I recommend this exercise for everyone. A feast of an infinite number of partial integrations and an infinite number of limit calculations, still leading to an amazingly simply and beautiful result. [integration of x^x between 0 and 1 is slightly less beautiful].

Elas, Mathematica fails in giving this answer. Is Geogebra able to do the job?

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maxima and geogebra are according (more or less), but CAS fails

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Hi, with the CAS, the integral with numeric evaluation is not bad :

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what version?. CAS of 5.0.238 does not work for me (not with integral[] or Nintegral[])

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Hi, i use 5.0.238.0 linux amd and it seems that we have the same on the web : https://www.geogebra.org/m/cxcgGjHk

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The GG numerical result is certainly pretty accurate as shown by the more basic calculation [Sequence[1 / i^i, i, 1, n]]

But my point is a more philosophical one. (Or more from a didactic point)

This is a nice example showing that useful computer programs like GG and Mathematica fail to demonstrate the astonishing beauty of mathematics in contrast to calculus. It is nice to know that this area is almost 1,29113 but the fact that it can be expressed in such a beautiful expansion is missed by computer programs. Try Wolfram Mathematica f.e.

That is the what I was trying to address.