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Evaluate: int(dx)/((x-1)xsqrt(x^(2)-1)...

Evaluate: `int(dx)/((x-1)xsqrt(x^(2)-1)`

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`int(dx)/((x-1)xsqrt(x^(2)-1)) ("put" x-1=1/t rArr dx=-1/t^(2)dt)`
`rArr I=int(-1/t^(2)dt)/(1/2sqrt(1/t+1)^(2)-(1/t+1)-1) = int(-dt)/sqrt(-t^(2)+t+1) = int(-dt)/sqrt(sqrt(5)/(2))^(2)-(t-1/2)^(2)`
`=-sin^(-1)(t-1/2)/(sqrt(5)/2) + C=-sin^(-1)(2t-1)/(sqrt(5))+C`, where `t=1/(x-1)`
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