Evaluate :(i) Integral of dx/(x^2 + 2x + 2) in (-infinity, +infinity)

Evaluate :
(i) Integral of dx/(x^2 + 2x + 2) in (-infinity, +infinity)
(ii) Integral of dx/x.sqrt(x^2 - 1) in (sqrt(2), +infinity)
(iii) Integral of dx/((sinx)^3).sqrt(cosx) in (0, pi/2)

[@aimplayers9366]

Sir probability question sir
Yeshwanth sir

[@AnkitKumarIITKGP]

@aimplayers9366, Probability solution: th-cam.com/play/PLEzs2Orn639LhygrS1VFTRR2cHzffcQ3s.html&si=_sjyJ4sAx_Jxf6Fp