i need to prove the next identities for 0<x<1:(adsbygoogle = window.adsbygoogle || []).push({});

∞

∫t^(x-1)/(1+t)dt=π/sin(πx)

0

1

∫t^(x-1)(1-t)^(-x)dt=π/sin(πx)

0

for the second one, my text gives me a hint to substitute t=u/(u+1), but i didnt succeed in getting the rhs.

i tried the defintion of B(x,1-x)=Gamma(x)Gamma(1-x)

but i dont know how to proceed from there.

thanks in advance.

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# Proving identities.

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