Nice integral problem

Find $\lim \limits_{n\to\infty} \int_{\ln(n)}^{\ln(n+1)} \frac {\int_π^x \int_π^v \cos(\ln(f(u)f(v))) \,du \,dv} {\int_π^x \int_π^v \sin(\ln(f(u)f(v))) \,du \,dv} \,dx$ where $e^x=\frac{\int_π^x \cos(\ln(f(t))) \,dt} {\int_π^x \sin(\ln(f(t))) \, dt}$