How Do You Integrate 1/(1+a*cos(x))?

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SUMMARY

The integral of the function 1/(1+a*cos(x)) can be efficiently computed using Wolfram Alpha, as manual calculation involves complex integration by parts and the inverse hyperbolic tangent function. The substitution t = tan(θ/2) is recommended as a standard technique to simplify the integration process. While some may view using computational tools as cheating, it is a practical approach to avoid unnecessary complexity in calculations.

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Homework Statement



How to integral this one?

1/(1+a*cosx)



Homework Equations





The Attempt at a Solution

 
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In this case, you use wolframalpha.com because the calculation by hand is brutal.

http://www.wolframalpha.com/input/?i=integrate+(1%2Ba*cos(x))^-1

Some people think that's cheating, but I think doing the grunt work here would be a waste of time since there's no new insight. From the looks of it, it's just several cumbersome integration by parts with the inverse hyperbolic tangent function.
 
I would try [tex]t=\tan (\theta /2)[/tex], it's one of the standard ones.
 

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