integration using PSQL algorithm

*To*: mathgroup at smc.vnet.net*Subject*: [mg52332] integration using PSQL algorithm*From*: Arturas Acus <acus at itpa.lt>*Date*: Wed, 24 Nov 2004 02:32:03 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Dear group, I have some reasons to suspect that some integral may have closed form in terms of powers of Pi: a+b*Pi+c*Pi^2+d*Pi^3+e*Pi^4 (a,b,c,d,e being algebraic numbers, probably with a=d=0). Assuming I can calculate the integral numerically to desired precision, is it possible to verify this hypothesis. As far as I know, the PSLQ algorithm, which helps to find algebraic relations between real numbers, can be useful here. The only (Mathematica related) reference I know is http://library.wolfram.com/infocenter/MathSource/4263/ , but the example here is too simple. As for details, the integral in consideration is integral = (-6*(-1 + a)*(4*Sqrt[7 + a] + Sqrt[2]*(5 + a)*Pi))/((5 + a)*(7 + a)^(3/2)) - (24*(-1 + a)*(6 + a)*Log[6 + a - Sqrt[5 + a]*Sqrt[7 + a]])/((5 + a)*(7 + a))^(3/2) with a= Cos[4* phi], integrated from 0 to Pi/2 (or to 2 Pi, no matter) The problems arises from second term. Mathematica 5.0 can't do it symbolically. How about 5.1? Sincerely, -- Arturas Acus <acus at itpa.lt>