Thanks for the suggestion Archie, but I still haven't cracked it.

After working with the project more, it turns out I'm looking for the solutions to 3 specific integrals related to the form above. They are: \(\displaystyle \int_{a}^{b}\frac{\cos \frac{2\pi x}{k}}{2*\left ( 1-\cos \frac{1}{k} \right )}dk\), \(\displaystyle \int_{a}^{b}\frac{\cos \frac{1}{k}}{2*\left ( 1-\cos \frac{1}{k} \right )}dk\), and \(\displaystyle \int_{a}^{b}\frac{\left | \cos \frac{2\pi x}{k}-\cos \frac{1}{k} \right |}{2*\left ( 1-\cos \frac{1}{k} \right )}dk\).

And yes, x is a constant, k is the variable, and the 3rd one numerator is an absolute value . Any help is appreciated.