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Re: An open letter

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16595] Re: [mg16540] An open letter
  • From: "David Park" <djmp at earthlink.net>
  • Date: Wed, 17 Mar 1999 23:55:04 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Jack,

You are right. It is sometimes frustrating trying to illustrate simple
steps that Mathematica does automatically.

I have attached a notebook which shows a ByPartsRule which will do
what you want, i.e., show the integration by parts rule as two steps.
It is too long to put in the MathGroup reply, but here is the rule
with one example.

ByPartsRule[f_]=HoldForm[Integrate[integrand_, x_]] :>
  Module[{diff, intg, g},
   g=Simplify[integrand/f];
   diff=D[f,x];
   intg=Integrate[g,x];
   f intg - (HoldForm[Integrate[b, x]] /.b :> Evaluate[intg diff])
  ]

HoldForm[Integrate[x Sin[x/2],x]] /.ByPartsRule[x]
-2 x Cos[x/2] - Integrate[-2 Cos[x/2], x]


(%+C)//ReleaseHold
C - 2 x Cos[x/2] + 4 Sin[x/2]

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/



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