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int0^1 (log x)/(sqrt(1-x^2))dx...

`int_0^1 (log x)/(sqrt(1-x^2))dx`

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`x= sin theta,`when x=0; x=1,`theta= pi/2`
I=`int_(0)^(pi/2) (log(sin theta))/cos theta * cos theta d theta `
`= int_0^(pi/2) log (sin theta) d theta`
`I= int_0^(pi/2) log ( cos theta) d theta`
`2I= int_0^(pi/2) log (2 sin theta cos theta)/2 d theta`
`= int_0^(pi/2) [log(sin 2 theta) - log 2] d theta`
`= int_0^(pi/2) log(sin 2 theta) d theta - int_0^(pi/2) log (2) d theta`
`2 theta = y`
...
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