25: The justification succeeds:

You get

Since the test integral converges, so does the given integral.

Note that the arctangent causes no troubles around infinity, so it is possible to just ignore it and use the test function g(x) = 1/x³. Now the justifying limit will not be equal to 1, but it will still be a non-zero number and so the Limit comparison test applies. This again shows that non-zero multiplicative constants play no role in limit comparison.

Answer