So the question is find value such that converges. Let's start to evaluate this improper integral as following:

Now consider the expression , since the highest power of in the numerator is 1 (note that ), we need the highest power of in the denominator also to be 1 in order for the limit to converge. Otherwise, as , the expression will either goto or , in either cases, the limit diverges. Hence when , the given integral converges.

Roy