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2h
comment Finding the limits when integrating a complex number
I do not believe $f$ to be analytic. Then the integral between the two points is path-dependent. I take it somewhere in the problem there is a specification that the integral is to be taken over a straight line between the endpoints.
1d
revised Inverse Laplace transform $\mathcal{L}^{-1}\left \{ \ln \left ( 1+\frac{w^{2}}{s^{2}}\right ) \right \}$
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2d
answered residue of a contour integral with a branch point on the boundary
2d
answered Inverse Laplace transform $\mathcal{L}^{-1}\left \{ \ln \left ( 1+\frac{w^{2}}{s^{2}}\right ) \right \}$
2d
answered Given $z$ show that $\left | z\right | = 2\sin\theta$ and $\arg z = \theta$
2d
comment Integration of hyperbolic functions.
The integral is not convergent; there is a non-integrable singularity at $x=0$.
May
20
revised Computing $\int_{0}^{+\infty}\frac{\log(x)}{\sqrt x(1+{x^2})}dx$.
edited tags
May
19
answered Computing $\int_{0}^{+\infty}\frac{\log(x)}{\sqrt x(1+{x^2})}dx$.
May
18
comment How do you find the inverse Laplace transform of $\frac{1}{\sqrt{s}(s-a)} $
math.stackexchange.com/questions/1009697/…
May
18
comment The Laplace transform of $\exp(t^2)$
The integral you have written doesn't converge. Dawson's function concerns integrals with finite limits.
May
17
comment Evaluate $\int_{|C|=2} \frac{dz}{z^2 + 2z + 2}$ using Cauchy-Goursat
@NavyColors_Blue: I have no idea what you are talking about. You seemed to state that you wanted an integral over a circle of radius $2$, so what this has to do with an integral over the real line i cannot say. Please explain what it is you want
May
17
answered Evaluate $\int_{|C|=2} \frac{dz}{z^2 + 2z + 2}$ using Cauchy-Goursat
May
17
comment Integral evaluation $\int_{-\infty}^{\infty}\frac{\cos (ax)}{\pi (1+x^2)}dx$
@Andrew: the stuff you have seen me publish here is pretty much a hobby. When I was an active researcher/engineer, I occasionally got to work on an analytical derivation of a result involving an integral. Thus, however, was rare. Mostly, practical applications involve a) integrals that are well-known, b) integrals done vis Mathematica or available in Gradshteyn & Rhyzik, or c) numerical work. Occasionally, I would work on asymptotic approximations. Maybe in theoretical physics you would get tough integrals like what we see here, but what we do is basically for fun.
May
17
answered Find $S=\sum_{n=-\infty}^{\infty} \frac{(-1)^n}{1+n^2}$
May
17
revised How i can find the fourier transform of $\frac{\sinh(ax)}{\sinh(\pi x)}$ where,$ |a| < \pi$
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May
16
awarded  Guru
May
16
comment Solving linear differential equation $t\dot{x}(t)+3x(t)=-\frac{1}{t^2+1}$
@Rzeta: yes, and that would be subsumed into your constant of integration.
May
16
answered Solving linear differential equation $t\dot{x}(t)+3x(t)=-\frac{1}{t^2+1}$
May
16
awarded  Nice Answer
May
16
revised How i can find the fourier transform of $\frac{\sinh(ax)}{\sinh(\pi x)}$ where,$ |a| < \pi$
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