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Re: Manually tell Mathematica how to evaluate integrals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128797] Re: Manually tell Mathematica how to evaluate integrals
  • From: "Dave Snead" <dsnead6 at charter.net>
  • Date: Tue, 27 Nov 2012 03:30:49 -0500 (EST)
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  • References: <20121125100031.218B0687C@smc.vnet.net>

You can put in your own integration formula:

Unprotect[Integrate];

Integrate[x_ PolyLog[n_, Exp[x_]], x_] :=
x PolyLog[n + 1, Exp[x]] - x PolyLog[n + 2, Exp[x]]

Protect[Integrate];

Then
Integrate[(x + a) PolyLog[n, b Exp[c x]], x]
will integrate

Cheers,
Dave Snead





-----Original Message----- 
From: Hui
Sent: Sunday, November 25, 2012 2:00 AM
To: mathgroup at smc.vnet.net
Subject: [mg128797] Manually tell Mathematica how to evaluate integrals

Hi all,

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

Integrate[x PolyLog[n,Exp[x]],x]

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

x PolyLog[n+1,Exp[x]] - x PolyLog[n+2,Exp[x].

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

Integrate[(x+a) PolyLog[n,b Exp[c x]],x].

Thank you very much, your assistance is much appreciated!

Hui





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