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A 2 dimensional integral in polar coordinate [closed]

Recently I got stuck on a 2 dimensional integral in polar coordinate, the expression is the following: $I(x)=\lim_{\xi\rightarrow0^+}\int_0^\infty dr\int_{-\pi/2}^{\pi/2}dt\frac{2\xi ^{2-2 x}r^{2x+1} \...
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