Hi,
I've just seen an article on a high accuracy numerical integration method that I hadn't heard of in http://www.codeproject.com/Articles/31550/Fast-Numerical-Integration (links to [3])
This is the techniques of "The double-exponential transformation in numerical analysis" by Masatake Mori and Masaaki Sugihara in the Journal of Computational and Applied Mathematics, volume 127 (2001), pages 287-296 [1]. Its discovery is in [2].
I've often seen mathcad integrals "fail" when folk forget that they have plotted some log-log function that ends up as a spike on a lin-lin plot. I'm not yet sure how well this technique would work within mathcad, but I thought it worth sharing.
Has anyone else used or studied this method? If it overcomes the lo-log problem it would be great.
Philip.
refs:
[1] http://www.sciencedirect.com/science/article/pii/S037704270000501X (I was able to download it)
[2] http://www.kurims.kyoto-u.ac.jp/~okamoto/paper/Publ_RIMS_DE/41-4-38.pdf Discovery of the Double Exponential Transformation and Its Developments.
[3] http://www.johndcook.com/double_exponential_integration.html