$\int \frac{f^{'}(x)}{f(x)}dx=$

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

$\int \frac{f^{'}(x)}{f(x)}dx=$

Options:

$\log |f(x)|+c$

$\log |f^{'}(x)|+c$

$\log |\frac{f(x)}{f^{'}(x)}|+c$

none

Correct Answer:

$\log |f(x)|+c$

Explanation:

Put $f(x)=t$

$ f'(x) . dx = dt$

$\Rightarrow \int{\frac{dt}{t}} = lnt + C = ln |f(x)| + C$$