For $X_1,...,X_n$ i.i.d. continuously distributed random variables with Lebesgue density $f_{\theta}(x)=\theta(\theta+1)x^{\theta-1}(1-x)\mathbf{1}_{(0,1)}(x)$ (Note: $\mathbf{1}_{(0,1)}(x)$ is an indicator function), How can I find the fisher information for a single observation?
For the Fisher information, I know the formula is $I(\theta)=-E_{\theta}\left[\frac{\partial^2}{\partial\theta^2}\ln f_{\theta}(X_1)\right]$ or alternatively $I(\theta)=E_{\theta}\left[(\frac{\partial}{\partial\theta}\ln f_{\theta}(X_1))^2\right]$. However, I can't solve for the partial derivative of $ln f_{\theta}(X_1)$ and how can I then find the expectation of this? I am very confused on this and I can't seem to find much information or examples of finding fisher information.