# Definite Integral to Infinity of Power of x over 1 + x/Proof 2

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## Theorem

- $\ds \int_0^\infty \dfrac {x^{p - 1} \rd x} {1 + x} = \frac \pi {\sin \pi p}$

for $0 < p < 1$.

## Proof

This theorem requires a proof.In particular: We can probably use Reduction Formula for Primitive of Power of x by Power of a x + b but I can see it being a long slogYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |