Question

Evaluate: $\int \frac{dx}{{(x-1)}^2}$

Answer 1

$\int \frac{dx}{(x-1{)}^2}$

let $x-1=u$

$dx=du$

$=\int \frac{du}{u^2}$

$=\int u^{-2}du$

$=\frac{u^{-1}}{-1}$

$=-\frac{1}{u}+c$

$=-\frac{1}{x-1}+c$