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

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• 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)
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```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)
>

```

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