Question

How to solve \[ \int_0^{2\Pi} \frac{dx}{(a+bCos(x))^2} \]

Answer 1

Any restrictions on \(a,b\) ? I'm assuming both are non-zero, but are they necessarily distinct?

Related to that, after plugging in some values for \(a\) and \(b\), it seems the integral only converges when \(a>b\). (using WolframAlpha's integration feature, of course; still not sure how to approach this by hand)

Answer 2

dude that thing cause me a real headache, I tried my best but eventually I got something but I was really bored of writing and thinking so I left the rest for you lol, I've attached my answer I hope it's clear enough...
also I agree with @SithsAndGiggles about the conditions of the constants, a must be bigger than b to make this integral convergent ,I concluded that because at a some level I got the integral multiplied by \[\sqrt{a ^{2}-b ^{2}}\] so I think it makes sense .. anyways you can complete the answer by partial fractions or by any other method..

Answer 3

@Ahmad1, I had a feeling the Weierstrass sub might be a viable option.

Answer 4

oh my friend @SithsAndGiggles , I am sorry, i'm taking the calculus|| course next semester, so perhaps I don't know what the Weierstrass sub is, or maybe it's the name.
anyways I thought my method was very complicated if you have an easier way just bring it on :)

Answer 5

The Weierstrass sub was when you let \(t=\tan\left(\dfrac{x}{2}\right)\), if you were wondering.

Answer 6

aha, thank you :)