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Re: intelligent Integrate

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: intelligent Integrate
• From: withoff
• Date: Fri, 22 Jan 93 09:35:19 CST

> Subject: intelligent Integrate
> 
>  Hi MathGroup,
> 
>  The input
> 
>  Integrate[ f'[x] g[x] + f[x] g'[x],x]
>  gives f[x] g[x]. I think by a rule associated with Integrate.
>  But
>  Integrate[f'[x] g[x],x] + Integrate[f[x] g'[x],x]
>  also produces
>  f[x] g[x]. This is quite nice, but I do not understand how this
>  happens by looking at the standard Mma evaluation procedure.
>  Is there a hidden rule for Integrate over Plus?
> 
>  Thanks for an answer,
> 
>  Michael Trott
> 
>  trott at physik.tu-ilmenau.de

This works out because Integrate[f[x] g'[x],x] evaluates to
f[x] g[x] - Integrate[g[x] f'[x], x] and the two unevaluated
integrals cancel.  There are no "hidden" rules for Integrate
over Plus.  Integrate returns many partially integrated results
for exactly this reason.

Dave Withoff
withoff at wri.com