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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*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

**References**:**Manually tell Mathematica how to evaluate integrals***From:*Hui <e.schlemm@hotmail.de>