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- #1

- Jun 20, 2014

- 1,925

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Show that

$$\int_0^\infty \frac{x^\alpha \log x}{x^2 + 1}\, dx = \frac{\pi^2}{4} \frac{\sin(\pi \alpha/2)}{\cos^2(\pi \alpha/2)}\quad (0 < \alpha < 1)$$

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