`int 1/((x-1)sqrt(4x^2-8x+3)) dx` Find the indefinite integral

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Let's rewrite the integral by completing the square of the term in denominator,


Apply the integral substitution: `u=2x-2`







Again apply integral substitution: `u=sec(v)`




Use the trigonometric identity:`sec^2(x)=1+tan^2(x)`



`=inttan(v)/tan(v)dv`   assuming `tan(v) >=0`



Substitute back `v=arcsec(u)`  and  `u=(2x-2)`

and add a constant C to the solution,


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