Let f: R → R be defined as f(x)= {x^3/((1- cos 2 x)^2) log_e ((1+2 x e^-2 x)/((1-x e^-x)^2)), x ≠ 0; α, x=0}. If f is continuous at x=0, then α is…

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $\displaystyle f(x)=\left\{\begin{array}{cl}\frac{x^3}{(1-\cos 2 x)^2} \log _{\mathrm{e}}\left(\frac{1+2 x \mathrm{e}^{-2 x}}{\left(1-x \mathrm{e}^{-x}\right)^2}\right), & x \neq 0 \\ \alpha, & x=0\end{array}\right.$. If $\displaystyle f$ is continuous at $\displaystyle x=0$, then $\displaystyle \alpha$ is equal to: