$\int \frac{x - 2}{x^{2} - 4 x + 3} d x =$

log ∣ ∣ \sqrt{x^{2} - 4 x + 3} ∣ ∣ + c

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log | (x - 3) (x - 1) / + c

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x log | x - 3 | - 2 log | x - 2 | + x

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None

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Solution

The correct option is B $log ∣ ∣ \sqrt{x^{2} - 4 x + 3} ∣ ∣ + c$
$\int \frac{x - 2}{x^{2} + 4 x + 3} d x$

$= \frac{1}{2} \int \frac{2 x - 4}{x^{2} - 4 x + 3} d x = \frac{1}{2} \int \frac{d (x^{2} - 4 x + 3)}{x^{2} - 4 x + 3}$

$= \frac{1}{2} l o g | x^{2} - 4 x + 3 | + c$

$= \frac{1}{2} l o g | x^{2} - 4 x + 3 | + c$

$= l o g | \sqrt{x^{2} - 4 x + 3} | + c$ .

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