Any way to integrate tanx and get ln|secx| + c ?

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doblechivo

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I am asking because when I am asked to integrate tanx, I just rewrite it as sinx/cosx and take u=cosx, and my answer is -ln|cosx| + c ... Which is the same thing as ln|secx|... But I am just wondering if there is some step-by-step method that would actually lead the answer to directly being ln|secx|, or is that just a nice way to rewrite the -ln|cosx|, but there is no way to substitute by parts or do any other trick that would lead directly to ln|secx|?

Just wondering. Thank you.
 
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