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

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Multiplying the integrand 1/(1-sec x) by a form of 1, such as (1 + sec x)/(1 + sec x), can simplify the integration process. Attempts to use sec x + tan x or sec x - tan x resulted in complex expressions, indicating that choosing the right form of 1 is crucial. The discussion emphasizes the importance of selecting appropriate trigonometric identities to simplify the integrand effectively. Participants suggest exploring various forms of 1 to find a more manageable expression for integration. Ultimately, the right multiplication can lead to a clearer path for solving the integral.
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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?
 
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How about multiplying by (1 + sec x)/(1 + sec x)? Is that one you tried?
 

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