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Re: Extending Integrate[]

• To: mathgroup at smc.vnet.net
• Subject: [mg87764] Re: Extending Integrate[]
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 16 Apr 2008 07:17:30 -0400 (EDT)
• Organization: Uni Leipzig
• References: <fu4lnj$si9$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de

Hi,

for a new integration rule, give always the most general
pattern, i.e. in your case

Unprotect[Integrate]

Integrate[d_. + c_.*Sin[Sin[a_. + b_. x_]], x_] :=
  c*Jones[a, x]/b + Integrate[d, x] /; FreeQ[c, x]

and all works fine.

Regards
   Jens


Szabolcs Horv=E1t wrote:
> According to the documentation it is possible to extend Integrate[] wit=
h
> new rules:
>
> http://reference.wolfram.com/mathematica/tutorial/IntegralsThatCanAndCa=
nnotBeDone.html
>
> The specific example that is given is:
>
> Unprotect[Integrate]
>
> Integrate[Sin[Sin[a_. + b_. x_]], x_] := Jones[a, x]/b
>
> Now Integrate[Sin[Sin[3x]], x] will return Jones[0, x]/3
>
> But if I try an integrand that is just slightly more complicated,
> Mathematica returns it unevaluated:
>
> In[21]:= Integrate[a + Sin[Sin[x]], x]
> Out[21]= Integrate[a + Sin[Sin[x]], x]
>
> My question is:  Is it really possible to extend Integrate in an
> intelligent way?  The above example seems to be just simple pattern
> matching.  It would work with any function, not just Integrate[].  Ther=
e
> is nothing new or surprising about it.
>
> But is it *really* possible to extend Integrate[] with new definitions
> in a way that Mathematica will use these rules when calculating more
> complicated Integrals?
>
> If (as I suspect) it is not possible to do this, then the documentation=

> is a bit misleading ...
>