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## Homework Statement

∫(0,1) √x/√[3]1-x

## Homework Equations

[itex]\Gamma[/itex]p[itex]\Gamma[/itex]q/[itex]\Gamma[/itex]p+q

## The Attempt at a Solution

p-1=1/2 →p=3/2

q-1=-1/3 →q=2/3

β(3/2,2/3)=[itex]\Gamma[/itex](3/2) [itex]\Gamma[/itex](2/3)/[itex]\Gamma[/itex](13/6)

[itex]\Gamma[/itex]3/2=1/2[itex]\Gamma[/itex](1/2)=√π/2

[itex]\Gamma[/itex]2/3=-1/3

[itex]\Gamma[/itex]13/6=7/6 1/6=7/36

β(3/2,2/3)=-6√π/7