Reciprocal of radical of a general quadratic: Find .

The absence of a radical sign and the presence of a positive coefficient of x² suggest using the integral leading to the Arctan.

Let's see if completing the square in the denominator helps:

. Substituting this result, we get

Let , , . Then I becomes

. Now we use the integral leading to the Arctan to get

. Finally, we express the result in terms of x: