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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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kcrisman gravatar imagekcrisman ( 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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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 gravatar imagekcrisman ( 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 gravatar imageMark ( 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 gravatar imageppurka ( 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 gravatar imagekcrisman ( 2012-11-29 03:27:54 -0500 )edit

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

Seen: 61 times

Last updated: Nov 28 '12