Integral question

08122017, 07:49 PM
Post: #1




Integral question
Is there any way to get ((pi)^2)/4 for the integral from 0 to pi of (x*(sin x))/(1+ (cos x)^2) ?


08132017, 12:15 AM
(This post was last modified: 08132017 12:44 AM by Helge Gabert.)
Post: #2




RE: Integral question
Yes, it can be done.
Note that arctan(1)arctan(0) is being recognized as the desired symbolic solution (pi^2/4). Just kidding. The hard part is to get there through some clever symmetrical substitution like u=pix, and some other substitutions, a shown here https://artofproblemsolving.com/communit...x__on_0_pi Not sure if that recognition pattern has been implemented in Giac/Xcas (maybe it is too expensive). 

08132017, 01:00 AM
Post: #3




RE: Integral question
(08122017 07:49 PM)lrdheat Wrote: Is there any way to get ((pi)^2)/4 for the integral from 0 to pi of (x*(sin x))/(1+ (cos x)^2) ? ibpu((x*sin(x)/(1+cos(x)^2)),x,x,0,π) Ceci n'est pas une signature. 

08132017, 01:24 AM
Post: #4




RE: Integral question
Excellent! Didn't think about ibpu and ibpdv. That'll do it.


08132017, 03:24 PM
Post: #5




RE: Integral question
Thanks!


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