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From: Mark McClure on 1 Jun 2010 04:20
On Sun, May 30, 2010 at 11:45 PM, Jesse Perla <jesseperla(a)gmail.com> wrote:
> I have an integral involving constants and an 'unknown' function. I
> would like to expand it out to solve for the constants and keep the
> integrals of the unknown function as expected.
> i.e.
> Integrate[a + z + s[z], {z, clow, chigh}]
>
> I want to get out:
> (a*chigh + chigh^2/2 - a*clow - clow^2/2) + Integrate[s[z], {z, clow,
> chigh}]

You could write a function that is explicitly linear but calls
Integrate otherwise. Here's a small modification of your example that
also illustrates constant multiples.

In[70]:== Clear[int];
int[expr_Plus, {var_, low_, high_}] :==
Map[int[#, {var, low, high}] &, expr];
int[expr_Times, {var_, low_, high_}] :== With[
{c == Select[expr, FreeQ[#, var] &]},
c*int[expr/c, {var, low, high}]];
int[expr_, {var_, low_, high_}] :== Integrate[expr,
{var, low, high}];
int[a + z + 5 c*s[z], {z, clow, chigh}] // InputForm

Out[74]//InputForm==
chigh^2/2 + a*(chigh - clow) - clow^2/2 +
5*c*Integrate[s[z], {z, clow, chigh}]

Mark McClure

From: Bob Hanlon on 1 Jun 2010 04:20

Integrate[#, {z, clow, chigh}] & /@ (a + z + s[z])


Bob Hanlon

---- Jesse Perla <jesseperla(a)gmail.com> wrote:

=============
I have an integral involving constants and an 'unknown' function. I
would like to expand it out to solve for the constants and keep the
integrals of the unknown function as expected.
i.e.
Integrate[a + z + s[z], {z, clow, chigh}]

I want to get out:
(a*chigh + chigh^2/2 - a*clow - clow^2/2) + Integrate[s[z], {z, clow,
chigh}]

However, FullSimplify, etc. don't seem to do anything with this. Any
ideas?


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