Re: Manually tell Mathematica how to evaluate integrals

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• Subject: [mg128835] Re: Manually tell Mathematica how to evaluate integrals
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Thu, 29 Nov 2012 06:06:47 -0500 (EST)
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```It's a nuisance but just do a change of variables

Integrate[Log[1 + (d + 1) Exp[x]] /.
d -> d - 1, x] /. d -> d + 1

-PolyLog[2, -(1 + d) E^x]

Integrate[Log[1 + (d + 1) Exp[x]], x] /.

Integrate[Log[1 + c_* Exp[x]], x] ->
(Integrate[Log[1 + temp* Exp[x]], x] /.
temp -> c)

-PolyLog[2, -(1 + d) E^x]

Bob Hanlon

On Wed, Nov 28, 2012 at 3:17 AM, Hui <e.schlemm at hotmail.de> wrote:
> Similar to my first question, I realised that Mathematica can evaluate the integral
>
> Integrate[Log[1 + d Exp[x]],x]
>
> but fails to find the anti-derivative of the function
>
> Log[1 + (d+1) Exp[x]].
>
> I find this quite annoying; does anyone a way around the issue?
>
> Any input is much appreciated.
> Thanks, Hui.
>
> Am Dienstag, 27. November 2012 08:38:48 UTC schrieb Hui:
>> Thank you DC. There is a typo in my original statement. I meant to suggest that
>>
>>
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>> x PolyLog[n+1,Exp[x]] - PolyLog[n+2,Exp[x]
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>> is the anti-derivative of the function
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>> x PolyLog[n,Exp[x]].
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>> That seems to be confirmed by differentiating the former expression.
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>>
>> Any ideas as to why Mathematica won't evaluate this integral, even in the explicit case of, say, n=4?
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>>
>> On Monday, November 26, 2012 4:40:54 AM UTC, DC wrote:
>>
>> > The following doesn't seem to reproduce your statement :
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>> > Simplify[D[x PolyLog[n + 1, Exp[x]] - x PolyLog[n + 2, Exp[x]], x],
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>> >  Assumptions -> {n \[Element] Integers, x \[Element] Reals}]
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>> > On Sunday, 25 November 2012 10:10:17 UTC, Hui  wrote:
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>> > > Hi all,
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>> > > I have a question about Mathematica's abilities to solve integrals. There seem to be cases where an antiderivative is explicitly known yet Mathematica fails to compute the integral. One example of this would be
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>> > > Integrate[x PolyLog[n,Exp[x]],x]
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>> > > which Mathematica only solves for n=1,2, even though it is quite easy to find a solution for higher values of n as well, namely
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>> > > x PolyLog[n+1,Exp[x]] - x PolyLog[n+2,Exp[x].
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>> > > I would like to know if it possible to teach Mathematica this integral in such a way that it will also recognise and solve it in more complicated cases such as
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>> > > Integrate[(x+a) PolyLog[n,b Exp[c x]],x].
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>> > > Thank you very much, your assistance is much appreciated!
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>> > > Hui
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>

```

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