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Prove that $$\int_{0}^{\infty} \frac{dt}{1+t^{n}}=\frac{\pi}{n}\csc\frac{\pi}{n}$$ Please help,I don't have a clue

user340586
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  • Are you familiar with the Residue theorem ? Try the "pizza slice" contour of angle $\frac{2\pi}{n}$. Try to show that the function tends to zero on the circular part of the contour as the radius tends to infinity. – M.G Jun 10 '16 at 19:14
  • I think this has been asked before. Did you search the site? – mickep Jun 10 '16 at 19:17
  • http://math.stackexchange.com/questions/781186/simplify-result-of-int-0-infty-frac11xndx – M.G Jun 10 '16 at 19:17
  • I've informed the moderators. – M.G Jun 10 '16 at 19:17
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    @M.G I think you can vote to close it instead. After 5 votes, it will be closed. – mickep Jun 10 '16 at 19:19

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