Can the Integral of 1/(1 + cosx)^2 be Simplified Further with Substitutions?

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The integral of 1/(1 + cosx)^2 has been calculated as (1/2)(tan(x/2)) + (1/6)(tan(x/2))^3 + C. There is curiosity about whether further simplification is possible through substitutions. Another participant attempted various substitutions for the same integral but found no success. The discussion highlights a need for a complete solution to the integral. The search for simplification methods continues among participants.
redshift
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Just finished working out the integral of 1/(1 + cosx)^2 as
(1/2)(tan(x/2)) + (1/6)(tan (x/2))^3 + C
I'm just wondering whether it's possible to use any substitutions to simplify this further.

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I think it's simple enough..
 
hi.
i've jux come across calculating the exact same integral (except that it's definite!). i tried to solve it using different substitutions bt all in vain. So. culd somebody post the complete solution here.
 
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