If the primitive of $\frac{1}{f(x)}$ is equal to $\log{\left\{ f(x) \right\}^{2} + c,\ then\ f(x)}$ is

Question

Dr. Abubacker · Accepted Answer

(b)
Given that, $\int_{}^{}{\frac{1}{f(x)}dx = \log{\left\{ f(x) \right\}^{2} + c}}$
$\Rightarrow \ \frac{1}{f(x)} = \frac{1}{\left\{ f(x) \right\}^{2}}2f(x)f^{'}(x)$
$\Rightarrow f^{'}(x) = \frac{1}{2}$
$\Rightarrow f(x) = \frac{x}{2} + d$
(where $d$ is a integration constant)

Q. If the primitive of $\frac{1}{f(x)}$ is equal to $\log{\left\{ f(x) \right\}^{2} + c,\ then\ f(x)}$ is

Explanation

Reviewed by Dr. Abubacker

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