With $f(x)=u(x)+iv(x)$ and $f(x)^*=f(-x)$, show that as $x_0 \to \infty$,
a) $u(x_0)\sim -\frac{2}{\pi x_0^2}\int_0^\infty xv(x)dx$
b) $v(x_0)\sim \frac{2}{\pi x_0}\int_0^\infty u(x)dx$
I'm following my course by reading Arfken's and Weber's Mathematical Methods for Physicists and this is one exercise on the topics of dispersion relations.
And although I have the solution manual for the book, the solution of this exercise (among others) is not listed in the manual.
I have no clue how to approach this. Any ideas?