Answer
$arcsec|2x-2|+C$
Work Step by Step
$\int \frac 1 {(x-1)\sqrt {4x^2-8x+3}}dx$
$\int \frac 1 {(x-1)\sqrt {(2x-2)^2-1}}dx$
$\int \frac 2 {(2x-2)\sqrt {(2x-2)^2-1}}dx$
$u=2x-2, du=2dx$
$\int \frac{du}{(u)\sqrt{u^2-1}}$
$\frac 1 a arcsec \frac {|u|} a +C$
$arcsec|2x-2|+C$
