1
$\begingroup$

Does anyone have any ideas on how to attack this:

$$\int_{0}^{\pi/2} \frac{\arctan^2 \left ( \sin^2 x \right )}{\sin^2 x} \, {\rm d}x$$

I cannot think of something that could work. Wolfram Alpha does not evaluate it either.

$\endgroup$
5
  • $\begingroup$ What makes you think there even is a solution in elementary functions? $\endgroup$ – Alfred Yerger Sep 10 '16 at 19:20
  • $\begingroup$ This integral was proposed by M.L.Glasser so I guess it has. I don't know where it was proposed though neither do I know any other details. $\endgroup$ – Tolaso Sep 10 '16 at 19:21
  • 7
    $\begingroup$ math.stackexchange.com/questions/1741089/… $\endgroup$ – nospoon Sep 10 '16 at 19:48
  • 1
    $\begingroup$ No way I would have derived that answer!.. Way beyond my league! Thanks @nospoon $\endgroup$ – Tolaso Sep 10 '16 at 19:52
  • 1
    $\begingroup$ @Tolaso Sure. You do ask very interesting questions, so keep it up. $\endgroup$ – nospoon Sep 10 '16 at 19:54