Since whenever r>0, it follows that . Substitute r=ax into that second integral to see that it is equal to . The integral can be evaluated (by contour integration, or by partial fractions), and it is equal to .

Putting that all together, you get . That is better than what was asked for, because it has an extra 2 in the denominator. But I don't see any way of getting this result by using the given hint about .