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Why does this not integrate

asked 2012-11-28 02:06:22 -0500

Mark gravatar image

why is this integral performed:

forget()
var('n')
assume(n>0)
integrate(1/sqrt(1+x^2*n),x,1,2)

i.e. I get:

-arcsinh(sqrt(n))/sqrt(n) + arcsinh(2*sqrt(n))/sqrt(n)

while this is not

forget()
var('n')
assume(n>0)
integrate(1/sqrt(1+x^2/n),x,1,2)
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Comments

This is now https://sourceforge.net/p/maxima/bugs/2507/

kcrisman ( 2012-11-28 03:57:26 -0500 )edit

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answered 2012-11-28 05:41:52 -0500

ppurka gravatar image

Somehow the simply_full() works. It probably forces the integration to happen.

sage: integrate(1/sqrt(1+x^2/n),x,1,2).simplify_full()
-(arcsinh(1/sqrt(n)) - arcsinh(2/sqrt(n)))*sqrt(n)
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Comments

Weird. It turns out that simplify_rational and simplify_radical do it, but not some of the others, and not just simplify (just passing to Maxima). But in Maxima itself, radcan and fullratsimp don't seem to have this effect; somehow the "nounform" is evaluated... weird.

kcrisman ( 2012-11-28 06:12:34 -0500 )edit

ehem, guys, for a newbs 1st-in-a-life-time three-liner typed into sage this is a little over my head. If this nobrainer integral results in a bug already, is your point that I should use integrate() only in conjunction with simplify_full()? Or is this a 'rare' case? Or am I doing something wrong?

Mark ( 2012-11-28 06:37:06 -0500 )edit

It should be considered a bug in my opinion. If the simplify process can make the integration happen, then the integration should have been performed in the first place, without the need for simplify.

ppurka ( 2012-11-29 02:55:25 -0500 )edit

Correct, and it's a Maxima bug, as far as I can tell, which I've reported upstream. This should definitely be a 'rare' case, since I've never heard of this happening before (not unevaluated integrals, which are legion, but this simplify behavior).

kcrisman ( 2012-11-29 03:27:54 -0500 )edit

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Asked: 2012-11-28 02:06:22 -0500

Seen: 54 times

Last updated: Nov 28 '12