Re: question about Mathematica integration function

*To*: mathgroup at smc.vnet.net*Subject*: [mg79854] Re: question about Mathematica integration function*From*: dimitris <dimmechan at yahoo.com>*Date*: Tue, 7 Aug 2007 01:26:11 -0400 (EDT)*References*: <f96ivj$q15$1@smc.vnet.net>

On 6 , 10:35, ingramfina... at gmail.com wrote: > I am having trouble integrating the following functions in > Mathematica. > > I have a two functions g and g1, where > > g = (x/(sigma*Sqrt[2*Pi*t^3]))*Exp[-(x-mu*t)^2/(2*sigma^2*t)] > > and > > g1= t*(x/(sigma*Sqrt[2*Pi*t^3]))*Exp[-(x-mu*t)^2/(2*sigma^2*t)] > > I assign values for sigma and mu, and then integrate g and g1 with the > limits of integration =BD and 1; I am trying to get an answer in terms > of x. If I use the Integrate function, Mathematica does not solve this > integral, it just restates the integral. If I assign a value for x, it > can numerically solve the integrals if I use NIntegrate, but this is > not very useful to me. In other words, I am trying to 'analytically' > integrate this function. > > I realize that I have asked a variation of this question earlier in > the forum, but I feel that if I explicate just what I am interested > in, it may be helpful. > > Any advice on how to get Mathematica (or any other software) to > generate the answer? Mathematica can't get a closed form for your integrals. In general... Explanation for such failure can be: 1) No closed form solution exists (for indefinite integrals, this is the case usually; for definite integrals some times). 2) Mathematica's integrator failed to express the closed form solution ( which exists and can be found either by the user-hard!-or by consulting to-easier!-the well known treatises in integral tables; see for example here http://amazon.com/s/ref=nb_ss_gw/105-4601676-4004465?initialSearch=1&url=search-alias%3Dstripbooks&field-keywords=%22tables+of+integrals%22&Go.x=3&Go.y=11 ) in terms of built in functions of Mathematica. In some cases helping a bit Mathematica might be important. 3) A closed form solution exists but it can be expressed in terms of special functions which are not implemented in Mathematica. Dimitris