If f(x).f((1)/(x))=f(x)+f((1)/(x)), and ...

If `f(x).f((1)/(x))=f(x)+f((1)/(x))`, and f(3)=82, then `int(f(x))/(x^(2)+1)dx=`

A

`x^(3)-x+2tan^(-1)x+c`

B

`(1)/(3)x^(3)-x+tan^(-1)x+c`

C

`(x^(3))/(3)-x+2tan^(-1)x+c`

D

`(1)/(3)x^(3)+x+2tan^(-1)x+c`

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The correct Answer is:

3

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