I have to find The energy of a signal using Rayleigh th. the signal is $$ x(t) = A e^{-At } u(t) $$ assuming A>0
Using the classic definition of E , I found that it should be $$ \frac{A}{2} $$
Using Rayleigh I should do $$ \int_{-inf}^{inf} | \frac{A}{A+i2\pi f}|^2 df $$ This because I previously found X(f) From this I obtained $$\frac{A^2}{8 \pi^2 f} log (\sqrt (A^2 +4\pi^2f^2)) $$ with log from -infinite to infinite.
$$ log \sqrt x = log \frac{x}{2} $$ but now I have no idea how to continue , and if this is correct.. thank you