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I am trying to integrate a function but the evaluation goes on and on forever.

Here is the code:

Integrate[
(Cos[x] Log[1 + x] + Sin[x]^2)/(2 x Cot[x] + ArcTan[x]^2), 
{x, 0, Pi/2}]

Is it because the function is not defined at $0$ nor $\pi/2$?

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  • 2
    $\begingroup$ There is likely no closed form. Of course you can perform NIntegrate and get the numerical answer ($0.709459$). $\endgroup$ – David G. Stork Jul 4 at 20:20
  • $\begingroup$ Ok thank you very much! $\endgroup$ – cigma Jul 4 at 20:41
  • $\begingroup$ on my pc it took 152 seconds (using the command 'Timing') to return the integral without evaluation!!!!! $\endgroup$ – logo Jul 4 at 20:43

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