How to evaluate this integral

∫[2,∞] ,dx / x^2+4

The answer must include π value.

Could you plz show me the steps? Thanks.

∫(x = 2 to ∞) dx/(x^2 + 4)
= lim(t→∞) ∫(x = 2 to t) dx/(x^2 + 2^2)
= lim(t→∞) (1/2) arctan(x/2) {x = 2 to t}
= lim(t→∞) (1/2) [arctan(t/2) - arctan 1]
= (1/2) (π/2 - π/4)
= π/8.

I hope this helps!