# Tagged Questions

Questions on the evaluation of integrals along a locus in the complex plane.

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### Contour integral to real integral: find suitable change of variables

There's probably simple solution but... I have a contour integral of the form $\int _{-i \infty}^{+i \infty} f(t) \ dt$. I want to make a transformation $t = g(s)$ so that the integral is real and of ...
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### Can somebody check whether I have calculated this contour integral correctly?

$$\int_{|z-\frac{1}{2}|=1}\frac{e^{-iz}}{z(z-1)(z^2-1)} dz$$ I used the Residue Theorem and got this answer: $2i\pi-\pi e^i -\frac{3}{2}\pi i e^i$ Is there also some software that can compute these ...
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### Can this integral be evaluated/approximated?

I've been trying to evaluate this integral without much success: $\displaystyle \int_{-\infty}^\infty dx\, e^{iax} \frac{1- e^{-c\sinh^2 bx}}{\sinh^2 bx}$ I've tried contour integration. There are no ...
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### Contour integration of a non-single valued complex function

Let $\xi>0$ and be real, $0<\alpha < 1$ and be real and $m\in\mathbb{N}$. Consider the integral on the complex plane z, $$\mathcal{F}(u) = \int_{\mathcal{C}}\exp(-(z\xi)^{\alpha})(u-z)^mdz$$ ...
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### Is this Complex Integration correct?

I want to integrate $\displaystyle \int_{-\infty}^\infty dx \, e^{iax}\frac{1-e^{-bx^2}}{x^2}$ for a>0. I am going to try and do this using the method of contour integration. I will choose a ...
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