If $g:\left[-2,2\right]\to R, \mathrm{where} f\left(x\right)=x^3+\tan x+\left[\frac{x^2+1}{P}\right]$ is an odd function, then the value of parametric P, where [.] denotes the greatest integer function, is

$g\left(x\right)=x^3+\tan x+\left[\frac{x^2+1}{P}\right]$

or $g\left(-x\right)=x^3+\tan \left(-x\right)+\left[\frac{{\left(-x\right)}^2+1}{P}\right]$

$=-x^3-\tan x+\left[\frac{x^2+1}{P}\right]$

Since g(x) is odd,

$g\left(x\right)+g\left(-x\right)=0$

$\therefore \left(x^3+\tan x+\left[\frac{x^2+1}{P}\right]\right)+\left(\begin{array}{l}-x^3-\tan x +\left[\frac{x^2+1}{P}\right] \\ \end{array}\right)=0$

or $2\left[\frac{\left(x^2+1\right)}{P}\right]=0 \mathrm{or} 0\le \frac{x^2+1}{P}<1$

Now, $x\in \left[-2,2\right]$

$\begin{array}{l}\therefore x^2+1\in \left[1,5\right]\\ \therefore P>5\end{array}$