Re: Help for an integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg57356] Re: Help for an integral*From*: "meznaric" <meznaric at gmail.com>*Date*: Wed, 25 May 2005 06:03:06 -0400 (EDT)*References*: <d6uspo$j5b$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

I think Mathematica uses the cumulative normal distribution function automatically (calling it Erf[x]). If you say try x/Exp[a*(1 - 2*x^2)^2], it will return a solution in terms of Erf function. You could also try a series solution, which would probably be in its simplest form if developed around x=1/Sqrt[2]. So you can try: int = Normal[Series[x^2/Exp[a*(1 - 2*x^2)^2],{x,1/Sqrt[2],10}]]; This will store the ten term Taylor series expansion into int and you can integrate it to obtain a numerical approximation for this integral. Well actually trying this out I found that NIntegrate works much better for the purpose of numerical approximation. If you wish to express the integral in terms of Erf, however, I am afraid you will have to do it by hand, because Mathematica does not seem able to do that (or there may be no way to do that). Sebastjan