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

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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 t=\tan (\theta /2), it's one of the standard ones.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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