Mathematics

if $$\int f(x) dx = f(x)$$, then $$\int {\left(\dfrac{f(x)}{f'(x)}\right)}$$. dx is equal to


ANSWER

x + c


SOLUTION
$$\displaystyle\int f(x)dx=f(x)$$
Differentiating on both sides
$$f(x)=f'(x)$$
$$\dfrac{f(x)}{f'(x)}=1$$
Applying integral on both sides
$$\displaystyle\int \dfrac{f(x)}{f'(x)}dx=\displaystyle\int dx=x+c$$.
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Single Correct Medium Published on 17th 09, 2020
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