Non-converging integral with linear transformation?!

*To*: mathgroup at smc.vnet.net*Subject*: [mg101047] Non-converging integral with linear transformation?!*From*: mereandor <mereandor at gmail.com>*Date*: Mon, 22 Jun 2009 04:23:24 -0400 (EDT)

Hi! I have a question regarding the Integral over the product of the two functions AiryAi and AiryAiPrime. Lets look at the following integrals: f[x_] = AiryAi[-1 + 10^5 x] AiryAiPrime[-500 + 10^5 x] NIntegrate[f[x], {x, 0, Infinity}] 10^-5*NIntegrate[f[x] /. x -> (10^-5 x), {x, 0, Infinity}] Mathematica 6 seems to be unable to evaluate the first one; the result is 0 and a warning about to slow convergence is issued. The second one is - as far as I know - the same as the first one but with a linear variable transformation applied -> this time the result is given without any warning. So basically my question is: what is going on there? Am I doing something wrong? thanks in advance for any hints ;)