Convergence and Integrals

Question

Let b be any real value and let’s write the integral. Find what values b could b

integral from negative to positive infinity of 1/(x²+bx +1)

Answer 1

If |b|≥2, the denominator will have real zeros and will, therefore not be integrable over the whole real line.

If |b|<0, then the integral will behave like an arctan and should be integrable over the whole real line.

In fact, if I compute the antiderivative correctly, the integral for these values of b is 0.

The antiderivative is K arctan {[x+(1/2)]/K} where K= (2/3)√3