The above integral has a pole at $x=-b$. $b$ is real and $b\ge 0$. To my knowledge such integral are solved using residue theorem. But, I am not able to find suitable contour to solve this integral.
How we can solve: $\int_0^\infty \frac{\exp(ib x) }{x+b}d x$
1
$\begingroup$
improper-integrals
-
0It seems there is no elementary result possible. See http://www.wolframalpha.com/input/?i=\int^{\infty}_{0}\frac{e^{ix}}{x%2Bb} – 2012-08-24
-
1Since $0$ has nothing special to do with the integrand, it is unlikely that contour methods will help. – 2012-08-24