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Re: Integral calculation!
Posted:
Mar 30, 2013 5:41 AM


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/cgibin/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 integrationjust 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



