\(\int\frac 1{(x -1 )^2 \sqrt{(1 - x)^2}}\,dx\)
\(= \int \frac{1}{(1 -x) (x - 1)^2}dx\)
\(= -\int \frac1{(x - 1)^3} \,dx\)
\(= -\int(x - 1)^{-3} \, dx\)
\(= - 1 \times\frac{(x - 1)^{-3 + 1}}{-3 + 1} + C\)
\(= \frac 12 (x -1)^{-2} + C\)
\(= \frac 1{2(x -1)^2} + C\)
