How to get this gaussian integral result?

*To*: mathgroup at smc.vnet.net*Subject*: [mg125808] How to get this gaussian integral result?*From*: simplerbysimpler at gmail.com*Date*: Tue, 3 Apr 2012 04:49:41 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Integrate[ x1^(n1) x2^(n2) x3^(n3) Exp[ a x1 x1 + b x2 x2 + c x3 x3 + d12 x1 x2 + d23 x2 x3 + d13 x1 x3 + d], {x1, -Infinity, Infinity}, {x2, -Infinity, Infinity}, {x3, -Infinity, Infinity}]. n1,n2,n3 are Natural numbers. I still cannot get the general result ,although mathematica takes so much time. Can you help me about this?