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RE: Why can't Mathematica do this simple integral ?

  • To: mathgroup at
  • Subject: [mg36819] RE: [mg36808] Why can't Mathematica do this simple integral ?
  • From: "DrBob" <drbob at>
  • Date: Fri, 27 Sep 2002 04:15:19 -0400 (EDT)
  • Reply-to: <drbob at>
  • Sender: owner-wri-mathgroup at

You would need to make assumptions about y, and you can't.  The function
and the limits have to take care of that, and when you try to do that,
you end up with an expression that has different antiderivatives on
different regions, for different values of x.  So, you have to break it
up.  The assumption x > 0 implies that x is real, so Im[x]==0 is

one = Integrate[Cosh[2 (y - x)] 
      2 y, {y, Min[x, 1/2], 1/2}, Assumptions -> {x > 0}];
two = Integrate[Cosh[2 (x - y)] 2 
      y, {y, 0, Min[x, 1/2]}, Assumptions -> {x > 0}];
one + two // FullSimplify
Plot[{one, two, one + two}, {x, 0, 1/2}];

 (1/4)*E^(-1 - 2*x)*(E + (-2 + E)*E^(4*x))

Bobby Treat

-----Original Message-----
From: Madhusudan Singh [mailto:spammers-go-here at] 
To: mathgroup at
Subject: [mg36819] [mg36808] Why can't Mathematica do this simple integral ?

        I have been trying to integrate the following :

        Integrate[Cosh[2 Abs[x-y]] 2 y, {y,0,1/2},

        However, Mathematica chokes and simply returns the integral as
it is. However, if I
 split up the integral into two portions, it quickly gives me an answer
for the parts. Is
 there something implicit that I am missing in the Assumptions ?



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