$\int \frac{f^{'} (x)}{f (x)} d x = log | f (x) | + C$

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Solution

$I = \int \frac{f^{'} (x)}{f (x)} d x .$
Let $f (x) = t; f^{'} (x) d x = d t$
$= \int \frac{d t}{t}$
$= log | t | + C$
$= log | f (x) | + c$ .

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