# Is this possible to integrate?

1. Jan 20, 2006

### jason17349

I haven't had any luck with mathcad and was wondering if this was possible to integrate...

$$\int_{0}^{2\pi} \frac {x+r*cos(\theta)}{(x^2+2r*x*cos(\theta)+r^2)^\frac {3}{2}} d\theta$$

Last edited: Jan 20, 2006
2. Jan 20, 2006

### daveb

It's certainly integrable...now whether you can solve it by non-numerical methods may be another matter entirely.

3. Jan 22, 2006

### jason17349

Does anybody have any suggestions on how to go about integrating this.... ? Or maybe explain why mathcad isn't able to integrate this..

4. Jan 22, 2006

### StatusX

Do you have to integrate over theta first? If you could integrate over x first, you could use substitution. That's usually the easiest way to do integrals like these.

5. Jan 22, 2006

### jason17349

Sorry, I should have said x and r are real non-negative constants..

6. Jan 22, 2006

### StatusX

Even so, you can pretend it's a variable. Then, integrate with respect to x to get some function F, so that your integral becomes:

$$\int \left( \frac{\partial}{\partial x} F \right) d\theta = \frac{\partial}{\partial x} \left( \int F d\theta \right)$$

I don't know if that helps, but it's a cool trick.

7. Jan 22, 2006

### benorin

8. Jan 23, 2006

### benorin

Maple gives an answer involving Elliptic integrals of the first and second kind, but in terms of those integrals, the answer is not that bad (though long enough for me not to post it.)