TITLE: compute an integral $\int {\frac{dx}{(x-1)\sqrt{x^2-3x+2}}}$
QUESTION [2 upvotes]: How we can compute this integral:
$$\int {\frac{dx}{(x-1)\sqrt{x^2-3x+2}}}$$
i know that the solution is:
$$I=\frac{2 (x-2)}{\sqrt{x^2-3x+2}}$$

REPLY [2 votes]: $x^2-3x+2=(x-1)(x-2)$. Substituting $t=x-1$, we have $\displaystyle\int\frac{dt}{t\sqrt{t~(t-1)}}$. Then let either 
$t=\cosh^2u~$ or $~t=\sec^2v$. The latter will yield $\displaystyle\int2\cos v~dv$, which is trivial.
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