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Integrate 1/(x-1)^2√(1-x)^2. |
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Answer» \(\int\frac 1{(x -1 )^2 \sqrt{(1 - x)^2}}\,dx\) \(= \int \frac{1}{(1 -x) (x - 1)^2}dx\) \(= -\int \frac1{(x - 1)^3} \,dx\) \(= -\int(x - 1)^{-3} \, dx\) \(= - 1 \times\frac{(x - 1)^{-3 + 1}}{-3 + 1} + C\) \(= \frac 12 (x -1)^{-2} + C\) \(= \frac 1{2(x -1)^2} + C\) |
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