Solving Intractable Integral: \frac{1}{(1+a cos(\theta - \phi))^2}

[Gib Z]

If you mean elementary anti derivative, then a) If you have limits of integration, numerical methods, or b) Define it as a new function ! =]

 

[NoobixCube]

Thanks for taking the time ice109

 

[coomast]

You can solve this integral by considering it after the simple substitution:

$$\theta- \phi=t$$

as:

$$\int\frac{dt}{(1+acos(t))^2}$$

Now use the substitution:

$$1+acos(t)=\frac{1-a^2}{1-acos(t)}$$

You will easily arrive at the solution.

Take a look at an older post of me where I explain this substitution a bit more:

https://www.physicsforums.com/showthread.php?t=204639

Hope this helps.