Help with Integral: Solve from 0 to pi

[pilopais]

I accept any suggestion in how to work out the integral below. It is a simplification of an integral over all k space. It had 16 terms and I am down to this 4. The idea is to integrate it from 0 to pi in respect of x, and y.

int{int{(-1-4 cos(x)^2*cos(y)^2+4cos(y)^2+cos(x)^2) / (1+4cos(y)^2+4cos(y)cos(x)dx}dy}

both with limits from 0 to pi.

Examples are:

int{int{sin(x)^2*cos(y)^2 dx}dy} = 1/4 pi.

I tried maple and matematica but didn't work. I strongly believe it is suppose to come out as a nice round integer number.

tks...

 

[colby2152]

$$\int{\int{/frac{(-1-4 cos(x)^2*cos(y)^2+4cos(y)^2+cos(x)^2)}{(1+4cos(y)^2+4cos(y)cos(x)}dxdy$$?

 

[pilopais]

Same integral (latex version)

Yeah, it looks llike:

$$\int_{0}^{\pi} \int_{0}^{\pi} \frac{-1-4 cos(x)^2 cos(y)^2+4cos(y)^2+cos(x)^2}{1+4cos(y)^2+4cos(y)cos(x)}dx dy$$

As explained before, this are the last terms of a 16 terms integral, all the other came to be integers.