- #1
Dustinsfl
- 2,281
- 5
\[
\int_0^{\infty}\frac{\cos(mx)}{(x^2 + a^2)^2}dx = \frac{\pi}{4a^3}e^{-am} (1 + am)
\]
The integral is even so
\[
\frac{1}{2}\text{Re}\int_{-\infty}^{\infty}\frac{e^{imz}}{(z + ia)^2(z - ia)^2}dz.
\]
Since the singularity is of order two, I believe I need to use
\[
\int\frac{f'}{f} = 2\pi\sum(\text{numer of zeros} - \text{number of poles})
\]
but I am not sure on how.
\int_0^{\infty}\frac{\cos(mx)}{(x^2 + a^2)^2}dx = \frac{\pi}{4a^3}e^{-am} (1 + am)
\]
The integral is even so
\[
\frac{1}{2}\text{Re}\int_{-\infty}^{\infty}\frac{e^{imz}}{(z + ia)^2(z - ia)^2}dz.
\]
Since the singularity is of order two, I believe I need to use
\[
\int\frac{f'}{f} = 2\pi\sum(\text{numer of zeros} - \text{number of poles})
\]
but I am not sure on how.