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

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The integral of 1/(1 + cos(x))^2 has been evaluated as (1/2)(tan(x/2)) + (1/6)(tan(x/2))^3 + C. Despite attempts to simplify this expression further using various substitutions, no additional simplifications have been successfully identified. The discussion highlights the challenges faced when trying to manipulate this integral beyond its derived form.

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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.

regards
 
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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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