# [Maxima] integral of cos(1/x) with range doesn't work.

Alexey Beshenov al at beshenov.ru
Tue Apr 8 14:47:13 CDT 2008

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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