My favourite integral problem
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?