Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
  • FAQ

Paper 2, Section II, A

Complex Analysis or Complex Methods | Part IB, 2012

By a suitable choice of contour show that, for −1<α<1-1<\alpha<1−1<α<1,

∫0∞xα1+x2 dx=π2cos⁡(απ/2)\int_{0}^{\infty} \frac{x^{\alpha}}{1+x^{2}} \mathrm{~d} x=\frac{\pi}{2 \cos (\alpha \pi / 2)}∫0∞​1+x2xα​ dx=2cos(απ/2)π​

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