How to calculate this integral for harmonic function?

[kakarotyjn]

I was asked to seek for a harmonic function u(x,y) in the 2-dimention disk whoes boundry condition is u\mid_C=A\cos(\phi),the I need to calculate the integral u(\rho_0,\theta_0)=\frac{1}{2\pi}\int_0^{2\pi}\frac{(R^2-\rho_0^2)A\cos(\theta)}{R^2-2R\rho_0\cos{(\theta-\theta_0)}+\rho^2}d\theta,but I don't know how to calculate.

Thank for any ideas

 

[JJacquelin]

With appropriate changes in coefficients, it is possible to transform the integral to the next know integral :