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Integrate the function
$\frac{1}{\sqrt{(x-1)(x-2)}}$
$\frac{1}{\sqrt{(x-1)(x-2)}}$
Solution:
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Verified Answer
$\int \frac{1}{\sqrt{(x-1)(x-2)}} d x=\int \frac{d x}{\sqrt{\left(x-\frac{3}{2}\right)^2-\left(\frac{1}{2}\right)^2}}$
$=\log \left|x-\frac{3}{2}+\sqrt{x^2-3 x+2}\right|+\mathrm{C}$
$=\log \left|x-\frac{3}{2}+\sqrt{x^2-3 x+2}\right|+\mathrm{C}$
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