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Bug integrating


Hola
If you make by hand the integral
Integrate[Cos[x]/Sqrt[-Log[Sin[x]]], {x, 0, Pi/2}]
it is Sqrt[Pi], which is the right value. (Make the change
Sin[x]=Exp[-t] and it goes Gamma[1/2]). 
But Mathematica CANNOT DO THIS: Its says -Sqrt[Pi] !!!
If you write it as
Integrate [Cos[x]/Sqrt[Log[1/Sin[x]]], {x, 0, Pi/2}]
Mathematica will get the right value
Try it

Saludos
Mariano


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