$\displaystyle I = \int_0^{4\pi} d\Omega \frac{exp(i \hat{n}\vec{a})}{1-(\hat{n}\vec{b})^2}$,
where a and b are fixed vector, and n is a unit vector pointing in the Omega direction.
In spherical coordinates $\displaystyle d \Omega = sin( \theta )d \theta d \phi$. But your integrand contains neither variable(?) So thus your integrand is constant with respect to both angles and can be taken outside of the integral.