Mathematics

$$\int { \cfrac { f'(x) }{ f(x) } dx } =\log { [f(x)] } +c$$


SOLUTION
Let $$f(x) =t$$

Differentiate on both sides ;

$$\Rightarrow f^{'} (x) dx=dt$$

Integral becomes : $$\dfrac {dt} {t} =log[t] +c$$

$$=log[f(x)] +c$$
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Subjective Medium Published on 17th 09, 2020
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