# Tagged Questions

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### Integral with rational functions of powers and exponentials

Any ideas how to solve: $$\int_0^\infty x^{n+\frac{1}{2}} (e^{a x }-1)^{-\frac{1}{2}} e^{i x t} dx$$ where $a$ and $t$ are real, positive constants; $n$ is a positive ...
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### How do you integrate Gaussian integral with contour integration method?

How do you integrate $$\int^{\infty}_{-\infty} e^{-x^2} dx$$ with contour integration method? I do not even know how to setup the problem.
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### Integrate $\int_0^\infty \frac{\sqrt{x}}{x^{2}+1}\, \mbox{d} x$

I've been trying to integrate the following $$\int_{0}^{\infty} \frac{\sqrt{x}}{x^{2}+1} \mbox{d} x$$ on half an annulus in the upper half plane. I keep getting $\frac{\pi}{\sqrt{2}}\ i$, which ...
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### Improper integration involving complex analytic arguments

I am trying to evaluate the following: $\displaystyle \int_{0}^{\infty} \frac{1}{1+x^a}dx$, where $a>1$ and $a \in \mathbb{R}$ Any help will be much appreciated.