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

[tennishaha]

Homework Statement

How to integral this one?

1/(1+a*cosx)

Homework Equations

The Attempt at a Solution

 

[Raskolnikov]

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.

 

[hunt_mat]

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