lim（x→+∞) [ (x+1)/(x²+1) ] arctanx
=lim（tan x→+∞) [ (tan x + 1)/(tan²x+1) ] arctan(tan x)
=lim(x→π/2) [sin x ·cos x + cos²x]·x
=lim(x→π/2) cos x(sin x + cos x)·x
=0·1·π/2
=0