The PSD of the received signal $r(t)$, under uniform scattering, is given by:
$$ S_r(f) = \cases {
\frac{P_r}{2 \pi f_D} \frac{1}{\sqrt{1 - (|f - f_c|/f_D)^2}} & \text{, if } |f - f_c| \leq f_D\cr
0 & \text{, otherwise }
}
$$
On every textbook I looked up (Wireless Communications by Andrea Goldsmith, p. 75 and a few others) it says that this PSD integrates to $P_r$, however, when I do the integration I always obtain $\infty$. My result seems to make sense as $S_r(f_c + f_D) = S_r(f_c - f_D) = \infty$.
My question is, how is it possible to obtain that the total power is equal to $P_r$ when the PSD integral goes to infinity?