Subject: integral of cos(1/x) with range doesn't work.
From: Alexey Beshenov
Date: Tue, 8 Apr 2008 23:47:13 +0400
On Tuesday 08 April 2008 21:59, Raymond Toy (RT/EUS) wrote:
>> (%i2) integrate(cos(1/x), x, 0, 2/%pi);
>> 2
>> ---
>> %pi
>> /
>> [ 1
>> (%o2) I cos(-) dx
>> ] x
>> /
>> 0
>>
>>
>> Why? Where is the failure of that it doesn't compute?
>
> What's the problem? The indefinite integral isn't in closed form either.
>
> Also, the definite integral uses different algorithms to compute it.
> Oftentimes it doesn't even try to do the indefinite integral first.
Actually,
integrate(cos(1/x),x) =
x*cos(1/x) + Si(1/x),
integrate(cos(1/x), x,0,2/%pi) =
2/%pi*cos(%pi/2) + Si(%pi/2) - limit(x*cos(1/x) + Si(1/x), x,0) =
Si(%pi/2) - %pi/2,
but now Maxima doesn't express integrals in terms of special integral
functions.
--
Alexey Beshenov <al at beshenov.ru>
http://beshenov.ru/
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