26: Around infinity the justification succeeds:

It follows that

Since the test integral converges, so does the one on the left.

Around x = 0 (from he right) the justification also succeeds:

It follows that

Since the test integral converges, so does the one on the left. Putting it together one gets that the whole given integral converges.

Note that this problem could have been also solved using the Comparison test. Indeed, for x > 0 one has

Answer