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

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 slog You 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.