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

Numerical Evaluation Of the Oscillatory Integral over exp(i*pi*x)*x^(1/x) between 1 and infinity

Numerical Evaluation Of the Oscillatory Integral over exp(ipix)*x^(1/x) between 1 and infinity