Reciprocal of radical of an exponential: Find.

The quantity under the radical sign looks like the form which leads to the Arcsec. However the usual factor in the denominator outside the radical appears to be missing. We shall see below that the missing factor is present after we make a substitution.

Let , , .

Solving for dx, we get .

By using the definition of u, we get .

Then I becomes

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

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

. Note that we don't need the usual absolute value sign because the exponential is always positive.