Answer
$\ln|x-1|+C$
Work Step by Step
$\displaystyle \int(x-1)^{-1}dx=$
Shortcut formula:
$\displaystyle \qquad\int(ax+b)^{-1}dx=\frac{1}{a}\ln|ax+b|+C$
Apply with $ \left[\begin{array}{l}
a=1\\
b=-1
\end{array}\right],$
$=\displaystyle \frac{1}{1}\ln|x-1|+C$
$=\ln|x-1|+C$
