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Integrate the functions(x-1)/(sqrt(x^2-1...

Integrate the functions`(x-1)/(sqrt(x^2-1))`

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` int(x-1)/(sqrt(x^(2)-1))dx " " underset( rArr x dx = (dt)/(2)) underset(rArr 2x dx=dt)underset(" Let " x^(2) -1=t)(" for first integration ")`
`= int (x)/(sqrt(x^(2)-1) )dx - int (1)/(sqrt(x^(2)-1))dx`
`=(1)/(2)int(1)/(sqrt(t))dt- int(1)/(sqrt(x^(2)-1^(2)))dx`
` =(1)/(2) intt^(-1//2)dt - int (1)/(sqrt(x^(2)-1^(2)))dx`
` =(1)/(2) .(t^(1//2))/(1//2) -log |x+sqrt(x^(2)-1^(2))|+c`
` =sqrt(x^(2)-1)-log |x+sqrt(x^(2)-1)|+c`
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