new to Mathematica. I am trying to approximate to ~30 decimal places $0<t<1$ satisfying $$\int_0^1 \frac{\sqrt{1-\sqrt x}}{\arctan(t + \arctan(x))} ~dx = \frac{\pi^2}{6}$$ I used the following code:
NSolve[Integrate[Sqrt[1 - Sqrt[x]]/ArcTan[t + ArcTan[x]], {x, 0, 1}] == Pi^2/6 && t > 0 && t < 1,t]
But the computation is taking very, very long. What am I doing wrong? How can I optimize this? A similar question has likely been asked before, but I do not know what to search for. Should I use NIntegrate
, somehow?