Date: Mar 30, 2013 5:41 AM
Author: Jose Carlos Santos
Subject: Re: Integral calculation!

On 30/03/2013 09:32, Ray Vickson wrote:

>> I need to calculate integral(0,pi/4) x.tan x dx.
>>
>>
>>
>> http://at.yorku.ca/cgi-bin/bbqa?forum=calculus;task=list

>
> Maple gets
> -(1/8)*pi*ln(2) + (1/2)*Catalan,
> where Catalan is Catalan's constant, equal to
> Catalan = sum{(-1)^n 1/(2n+1)^2,n=0..infinity} = 1 - (1/9) + (1/25) - (1/49) + ... =~= 0.9159655942.
>
> Numerically, the integral is about 0.1857845357, which is obtained both from the formula, and from a numerical integration---just as a check on Maple's work.


Mathematica gets the same thing. Of course, this suggests that x.tan(x)
doesn't have an elementary primitive.

Best regards,

Jose Carlos Santos