Question

If $f\left(x\right)$ is a polynomial satisfying $f\left(x\right).f\left(\frac{1}{x}\right)=f\left(x\right)+f\left(\frac{1}{x}\right)$, and $f\left(3\right)=82$, then $\int \frac{f\left(x\right)}{x^2+1}dx=$

• A. $x^3-x+2{\tan }^{-1}x+c$
• B. $\frac{1}{3}{x}^3-x+{\tan }^{-1}x+c$
• C. $\frac{x^3}{3}-x+2{\tan }^{-1}x+c$
• D. $\frac{1}{3}{x}^3+x+2{\tan }^{-1}x+c$

Answer 1

Answer: (A)

$x^3-x+2{\tan }^{-1}x+c$

Option (C) is the correct answer.