MLE of the exponent of a power density

Let $X_1,…,X_n$ be a random sample from a population with probability density function

$$f_\theta(x)=\begin{cases}(\theta+1)x^\theta, & 0<x<1,\ 0, & \text{otherwise,}\end{cases}$$

where $\theta>0$ is unknown. The maximum likelihood estimator of $\theta$ is