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Integrate[] crashes kernel

• To: mathgroup at smc.vnet.net
• Subject: [mg50733] Integrate[] crashes kernel
• From: math5bug at lmm.jussieu.fr (B. Oudoli)
• Date: Sat, 18 Sep 2004 05:48:47 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi all,
I've found a fairly simple integration that crashes mathematica kernel.
I'm trying to integrate symbolically the function x Cos[a x] with respect to x,
where the factor a can be symbolical or numerical.

Integrate[x Cos[a x],x]
   yields the correct answer: Cos[a*x]/a^2 + (x*Sin[a*x])/a
   note that this integral is perfectly regular for a->1

Integrate[x Cos[2. x], x]
   yields again the correct answer: 0.25 Cos[2. x] + 0.5 x Sin[2. x]

Integrate[x Cos[x], x]
   yields again the correct answer: Cos[x] + x Sin[x]

However, 
Integrate[x Cos[1. x], x]
   crashes the kernel, and it's impossible to abort or interrupt
   the calculation, which lasts forever.

This bug appears in mathematica 5, but not in mathematica 4.

I find it annoying that Integrate[] works for some real values of a, but
not for some other ones for which the integral behaves perfectly well.

Any remark ?