Question

Determine whether the integral converges or diverges, give the value if it converges.

Answer 1

First off, let's define a "b" that will allow us to better study the integral:
\[\int\limits_{1}^{\infty}\frac{ \tan ^{-1}x }{ x^2+1 }dx\]
We will take the limit as a new variable approaches infinity, so we can solve the integral and study the divergence or convergence of the result:
\[\lim_{b \rightarrow +\infty}\int\limits_{1}^{b}\frac{ \tan ^{-1}x }{ x^2+1 }dx\]

Answer 2

Once that is established do I have to find the integral of the problem?