1.

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

Answer»

Solution :`(x-1)/SQRT(x^2-1) = x/sqrt(x^2-1)-1/sqrt(x^2-1)`
if we put t = `x^-1`, we have
`DT = 2x DX GT XDX = dt/2`
therefore` int x/sqrt(x^2-1) dx = int 1/sqrtt dt/2 = sqrtt = sqrt(x^2-1)`
Thus, `int (x-1)/sqrt(x^2-1) dx`
= `sqrt(x^2-1)-log|x+sqrt(x^2-1|+c`


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