I have trouble understanding a part of the solution to this problem given in my book:
NOTE: $\mathrm{arccot} = $ "arc cotangent", it is not a typo.
Find for which p the integral is convergent.
$$
\int_{0}^{\infty}{x^{p}\,\mathrm{arccot}^{2}\left(\,x\,\right) \over
\left(\,x^{2} + 1\,\right)\ln^{3}\left(\,x + 1\,\right)}\,\mathrm{d}x.
$$
Since $$
\lim_{x\to 0^{+}}\,\,{x^{p}\,\mathrm{arccot}^{2}\left(\,x\,\right) \over
\left(\,x^{2} + 1\,\right)\ln^{3}\left(\,x + 1\,\right)}:
{1 \over x^{3 - p}}=\left(\,{\pi \over 2}\,\right)^{2}.
$$
Therefore
$$
\int_{0}^{2}{x^{p}\,\mathrm{arccot}^{2}\left(\,x\,\right) \over
\left(\,x^{2} + 1\,\right)\ln^{3}\left(\,x + 1\,\right)}\,\mathrm{d}x
$$
is convergent only when
$\displaystyle{\int_{0}^{2}{\mathrm{d}x \over x^{3 - p}}}$ is convergent
$\Longrightarrow p>2$.
Now the thing I dont understand in this part of the solution is why we choose two for a bound in the integal on the third row ?. It seems like an arbitrary number or maybe it is supposed to be arbitrary ?. I am confused and would appreciate help.