Question

If $\int f\left(x\right)dx=f\left(x\right),then\int \frac{f\left(x\right)}{f^{\prime }\left(x\right)}$ dx =

• A. x + c
• B. log f(x) = c
• C. log f(x) + c
• D. $e^f\left(x\right)+c$

Answer 1

The correct option is A x + c

$\int f\left(x\right)dx=f\left(x\right)$

differentiates on both sides

$f\left(x\right)=f^{\prime }\left(x\right)$

$\frac{f\left(x\right)}{f^{\prime }\left(x\right)}=1$

Applying integral on both sides

$\int \frac{f\left(x\right)}{f^{\prime }\left(x\right)}dx=\int 1dx=x+C$

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