Find the limit LIM (x → + ∞) ∫ [0, x] (arctant) & # 178; DT / √ (X & # 178; + 1)

Find the limit LIM (x → + ∞) ∫ [0, x] (arctant) & # 178; DT / √ (X & # 178; + 1)

Should the last X of the question be t? If so, the answer is as follows
lim(x→+∞)∫[0,x](arctant)²dt/√(t²+1)
=lim(x→+∞)∫[0,x](arctant)²d(arctant)
=lim(x→+∞)(arctant)³/3|[0,x]
=lim(x→+∞)(arctanx)³/3
=(π/2)³/3
=π³/24