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Topic: Manually tell Mathematica how to evaluate integrals
Replies: 5   Last Post: Dec 3, 2012 3:18 AM

 Messages: [ Previous | Next ]
 Bob Hanlon Posts: 906 Registered: 10/29/11
Re: Manually tell Mathematica how to evaluate integrals
Posted: Dec 3, 2012 3:18 AM

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@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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>

Date Subject Author
11/25/12 Eckhard Schlemm
11/25/12 DC
11/27/12 Eckhard Schlemm
11/28/12 Eckhard Schlemm
12/3/12 Bob Hanlon
12/3/12 Bob Hanlon