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Let f be a differentiable function sati...

Let f be a differentiable function satisfying `f(xy)=f(x).f(y).AA x gt 0, y gt 0` and `f(1+x)=1+x{1+g(x)}`, where `lim_(x to 0)g(x)=0` then `int (f(x))/(f'(x))dx` is equal to

A

`(X^(2))/(2)+c`

B

`(x^(3))/(3)+c`

C

`(x^(2))/(3)+c`

D

none of these

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The correct Answer is:
A
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