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