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## Main Question or Discussion Point

How does this:

[itex]\int_0^\infty\frac{x^{m-1}}{1+x} dx[/itex]

equal

[itex]\frac{\pi}{sin(m\pi)}[/itex]

?

It has been simply stated as a fact in a proof of the so called "Euler reflection formula" in a textbook.

I have tried the usual ways, substitution, integration by parts and even series expansion of 1/1+x but I can't find how the above equality is true.

[itex]\int_0^\infty\frac{x^{m-1}}{1+x} dx[/itex]

equal

[itex]\frac{\pi}{sin(m\pi)}[/itex]

?

It has been simply stated as a fact in a proof of the so called "Euler reflection formula" in a textbook.

I have tried the usual ways, substitution, integration by parts and even series expansion of 1/1+x but I can't find how the above equality is true.