- #1

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[tex]

\int_{0}^{\infty}{x^{\alpha - 1} \over x+1}={\pi \over sin\alpha\pi}

[/tex]

I used the standard keyhole contour around the real axis (taking that as the branch cut), but using the residue theorem I end up with:

[tex]

-\pi i e^{i\alpha\pi}

[/tex]

Which obviously doesn't match. Although this does match up for alpha equals one half.

Some help would be appreciated.