Let $X_1,...X_n$ be a sample from a distribution with probability density
$$p_{\theta} (x) = \theta (1+x)^{-(1+\theta)}, \text{ for } x \geq 0$$
and $0$ elsewhere , with $\theta >0 $ unknown. Determine the maximum likelihood estimator for $\theta$
After calculations, I lead to
$$\theta = \frac{n}{\sum_{i=1}^{n} log(1+x_i)}$$
Is there a way to simplify this more?