Quiz: calculating a definite integral

[Gerson W. Barbosa]

(01-01-2014 10:31 PM)Thomas Klemm Wrote:  

(12-31-2013 10:24 AM)peacecalc Wrote:  calculating the integrand: instead of \( x^{-x} \) as \( \exp(-x\cdot\ln(x)) \)

That's a step into the right direction.
What's the next? What's \( \exp(t) \)?

Cheers
Thomas

e^t=1+t+1/2*t^2+1/6*t^3+...
=1-x*lnx+x^2*(lnx)^2/2-...
which, upon integration over [0..1], yields
1+1/2^2+1/3^3+1/4^4+...
The first ten terms add up to
1.29128599706
Cheers from Camboriú, Brazil
Gerson.
PS: Sorry for not elaborating enough (slowly typing this on an iphone)
Ought to be at the beach instead :-)