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)
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)
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.
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?
Asked: 2012-11-28 09:06:22 +0200
Seen: 649 times
Last updated: Nov 28 '12
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This is now https://sourceforge.net/p/maxima/bugs/2507/
This is now fixed in the latest Sage beta (and probably before).