$\int \frac{d x}{x (l o g x - 2) (l o g x - 3)} = f (x) + c t h e n f (x) =$

$\frac{1}{x} l o g \frac{| l o g x - 3 |}{| l o g x - 2 |}$

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$l o g \frac{| l o g x - 3 |}{| l o g x - 2 |}$

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$2 l o g \frac{| l o g x - 3 |}{| l o g x - 2 |}$

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$l o g | (l o g x - 3) (l o g x - 2) |$

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Solution

The correct option is B
$l o g \frac{| l o g x - 3 |}{| l o g x - 2 |}$

$P u t l o g x = t$
$\Rightarrow I = \int \frac{1}{(t - 2) (t - 3)} d t$
$I = l o g ∣ ∣ \frac{l o g x - 3}{l o g x - 2} ∣ ∣ + c$

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