I would like to know how to integrate a function that looks like
$$ \int_{a<|x|<b} \frac{dx}{|x|^{-n-it}}, \quad x \in \mathbb{R}^n, \, 0<a<b. $$
Thank you.
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Are $a$ and $b$ real? – Jakobian Aug 21 '18 at 22:41
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Please clarify whether you are integrating with respect to $t$ or $x$. – Kavi Rama Murthy Aug 21 '18 at 23:38
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Yes a and b are real , I have corrected the integral. – Hazelnut Aug 22 '18 at 23:04
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Change to spherical coordinates in $\mathbb R^n$. The integral over the angles gives the surface area of a unit $(n - 1)$-sphere. – Maxim Aug 23 '18 at 00:48