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Solve definite integrals split into two integrals?

Hi, can someone help me in this perhaps trivial problem with integrals?

I want to use DSolve command to a simple differential equation: 

EDMQ = Q'[a] == -\[CapitalPi]M \[Gamma][a] + (\[Rho] + \[Delta]) Q[a]
DSolve[{EDMQ, Q[\[Omega]] == 0}, {Q[a]}, {a}]

The Solver gives me the solution splitted into two integrals: ApplyingDSolve

I would like to have it in a simpler form, as

enter image description here

Thank you in advance Alessandra
POSTED BY: Alessandra Buratto
3 Replies
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Alessandra,

  1. Please use the code format button (upper left) to post code because the code is corrupted with a normal paste.

  2. I think you need multiplication signs (*) between \[CapitalPi]*M*\[Gamma][a] (or spaces) but it is hard to tell if that was a copy-paste problem

  3. MMA is probably not certain that your integral exists at 1 (it may be a singularity) so it cannot generally make the simplification that you want (this is a guess on my part)

  4. you can make your own rule and apply that simplification:

    intrule = 
 Inactive[Integrate][f_, {x_, min_, max1_}] - 
   Inactive[Integrate][f_, {x_, min_, max2_}] -> 
  Inactive[Integrate][f, {x, max1, max2}]

EDMQ = (Q'[
     a] == -\[CapitalPi]*M*\[Gamma][a] + (\[Rho] + \[Delta]) Q[a]);
 an = DSolve[{EDMQ, Q[\[Omega]] == 0}, {Q[a]}, {a}]
an /. intrule

I hope this helps.

Regards,

Neil
POSTED BY: Neil Singer

Thank you Neil for your prompt suggestion. I will try to implement it. best Alessandra
POSTED BY: Alessandra Buratto

Dear Neil, it works! thank you again!
POSTED BY: Alessandra Buratto
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