Question

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

Answer 1

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

$=\int \sqrt{(x-\frac{3}{2}{)}^2+(\frac{1}{2}{)}^2}$

$=\frac{x-\frac{3}{2}}{2}\sqrt{(x-\frac{3}{2}{)}^2+(\frac{1}{2}{)}^2}+\frac{1}{2}(\frac{1}{2}{)}^{2}log|x-\frac{3}{2}+\sqrt{(x-\frac{3}{2}{)}^2+(\frac{1}{2}{)}^2}|+c$