Integral no longer evaluated in Version 7, 8

*To*: mathgroup at smc.vnet.net*Subject*: [mg114410] Integral no longer evaluated in Version 7, 8*From*: John Jowett <john.m.jowett at gmail.com>*Date*: Fri, 3 Dec 2010 05:22:51 -0500 (EST)

Hello, With Mathematica Version 7, the integral Integrate[(x^2/2)*BesselK[5/3, x], {x, 0, Infinity}] correctly evaluated to (8*Pi)/(9*Sqrt[3]). In Mathematica 7 or 8, it gives the message Integrate::idiv: Integral of x^2 BesselK[5/3,x] does not converge on {0,\[Infinity]}. >> I haven't been able to find any way to get this to work (NIntegrate works fine). Termwise integration of the asymptotic form of the integrand works but does not appear to converge. Can anybody explain why Mathematica lost this capability? It may have something to do with no longer recognising cancellations among expressions involving the Gamma function. Any ideas for getting the integral to work ? Thanks, John Jowett