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

Question

Evaluate:

$\int{\frac{dx} {\sqrt{x^{2} - 3x + 2}}}$

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Answer

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

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

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