Re: An analytical solution to an integral not currently in Mathematica?

*To*: mathgroup at smc.vnet.net*Subject*: [mg131374] Re: An analytical solution to an integral not currently in Mathematica?*From*: "Kevin J. McCann" <kjm at KevinMcCann.com>*Date*: Tue, 16 Jul 2013 05:56:25 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <krtdrb$rbm$1@smc.vnet.net>

If I take the answer the "other system" produces: f[x_] = -Sqrt[\[Pi]] I E^(-a x - b) Erf[I Sqrt[Log[x] + a x + b]] and compare f'[x] with the integrand for some choices of a,b,x, I do not get agreement. Kevin On 7/14/2013 1:44 AM, Sean McBride wrote: > Question: Integral dx of 1/sqrt(Log[x] + a*x + b) > (sorry if my notation is off; I just used the online integrator and don't have Mathematica proper, http://integrals.wolfram.com/index.jsp?expr=1%2Fsqrt%28Log%5Bx%5D+%2B+a*x+%2B+b%29) > (the online integrator returned this as of the time of writing this (2013-07-13): "Mathematica could not find a formula for your integral. Most likely this means that no formula exists." ) > > > Another system's unconfirmed answer (in that notation; sorry) (version 5.27.0): -sqrt(%pi)*%i*%e^(-a*x-b)*erf(%i*sqrt(log(x)+a*x+b)) > > Strangely, the other system only produces this result when given, say, x(t) in all places for x (including variable of integration). > > I can't seem to get the other system to verify its result symbolically, but when I try random numerical sampling, it does seem to agree, albeit horribly plagued by floating point errors for large x. > > > Can anyone offer insight, or possibly prove it's correctness or incorrectness? :) > > > (P.S. I just joined this group, so apologies if it's the wrong one or I'm not following guidelines) >