Evaluate : d x x^2-3 x+2 - Vidyadip

Question

Evaluate : $\int \frac{d x}{\sqrt{x^2-3 x+2}}$

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Answer

$\text { (b) : We have, } \int \frac{d x}{\sqrt{x^2-3 x+2}}=\int \frac{d x}{\sqrt{\left(x^2-3 x+\frac{9}{4}\right)-\frac{1}{4}}}$
$=\int \frac{d x}{\sqrt{\left(x-\frac{3}{2}\right)^2-\left(\frac{1}{2}\right)^2}}=\log \left|\left(x-\frac{3}{2}\right)+\sqrt{x^2-3 x+2}\right|+C$

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