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Topic: Manually tell Mathematica how to evaluate integrals
Replies: 1   Last Post: Nov 27, 2012 3:31 AM

 Dave Snead Posts: 52 Registered: 12/13/04
Re: Manually tell Mathematica how to evaluate integrals
Posted: Nov 27, 2012 3:31 AM

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,

-----Original Message-----
From: Hui
Sent: Sunday, November 25, 2012 2:00 AM
Subject: 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