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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, Dave Snead
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



