Reciprocal of radical of a general quadratic: Find .

This has a negative coefficient of x² and another factor in the denominator, suggesting the integral leading to the Arcsec.

Let's see if completing the square in the quantity under the radical sign helps:

. Substituting this result, we get

Let , , . Then I becomes

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

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