  Real and imaginary part of the limit 2N->infinity of the integral
int_{x=1..2N} exp(i*pi*x)*x^(1/x) dx are evaluated to 20 digits with brute
force methods after multiple partial integration, or combining a standard
Simpson integration over the first halve wave with series acceleration
techniques for the alternating series co-phased to each of its points. The
integrand is of the logarithmic kind; its branch cut limits the performance of
integration techniques that rely on smooth higher order derivatives.
