How to calculate generalized integral ∫ upper limit positive infinite lower limit negative infinite 1 / x ^ 2 + 4x + 5 DX?

A:
(-∞→+∞) ∫ 1/(x²+4x+5) dx
=(-∞→+∞) ∫ 1/[(x+2)²+1] d(x+2)
=(-∞→+∞) arctan(x+2)
=π/2-(-π/2)
=π

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