How Can Multiplying by a Form of 1 Simplify Integrating 1/(1-sec x)?

[Whitishcube]

Homework Statement

Integrate 1/(1-secx)dx by multiplying the integrand by a form of 1.

Homework Equations

any sort of trig identity?

The Attempt at a Solution

I've tried multiplying by forms of 1 such as secx+tanx, secx-tanx, and others, but when i do, i just end up with a messy looking integrand.
any pointers with this and any other problems like it?

 

[Mark44]

How about multiplying by (1 + sec x)/(1 + sec x)? Is that one you tried?