$\cfrac{1}{{\sqrt {\left( {x - 1} \right)\left( {x - 2} \right)} }}$

Let$= \int {\cfrac{1}{{\sqrt {\left( {x - 1} \right)\left( {x - 2} \right)} }}} dx = \int {\cfrac{{dx}}{{\sqrt {{x^2} - 3x + 2} }}}$

$= \int {\cfrac{{dx}}{{\sqrt {\left( {{x^2} - 2 \cdot \cfrac{3}{2}x + \cfrac{9}{4}} \right) + 2 - \cfrac{9}{4}} }}} = \int {\cfrac{{dx}}{{\sqrt {{{\left( {x - \cfrac{3}{2}} \right)}^2} - \cfrac{1}{4}} }}}$

$= \int {\cfrac{{dx}}{{\sqrt {{{\left( {x - \cfrac{3}{2}} \right)}^2} + {{\left( {\cfrac{1}{2}} \right)}^2}} }}} = \log \left| {\left( {x - \cfrac{3}{2}} \right) + \sqrt {{{\left( {x - \cfrac{3}{2}} \right)}^2} - {{\left( {\cfrac{1}{2}} \right)}^2}} } \right| + C$

$= \log \left| {\left( {x - \cfrac{3}{2}} \right) + \sqrt {\left( {x - 1} \right)\left( {x - 2} \right)} } \right| + C$