I was studying a book called Theoretical Astrophysics by Prof T Padmanavan, and in the very first chapter, i find the expression of Net Contributing Pressure ($P$) as:

$$P = \frac{1}{3} \int\_{0}^{\infty}n(\epsilon)p(\epsilon)v(\epsilon)d\epsilon$$

followed by relativistic momentum $P = \gamma mv$ and kinetic energy, $\epsilon = (\gamma-1)mc^2$ with $\gamma$ as the relativistic factor. By far this I understood it, but then, substituting these values in the above given expression, as:

$$P = \frac{1}{3} \int\_{0}^{\infty}n\epsilon\left(1+\frac{2mc^2}{\epsilon}\right)\left(1+\frac{mc^2}{\epsilon}\right)^{-1}d\epsilon$$

is not understood by me. Can anyone please help me out with proper steps to achieve this expression. Thanks in advance !

[![enter image description here](https://i.stack.imgur.com/UFI19.png)](https://i.stack.imgur.com/UFI19.png)
[![enter image description here](https://i.stack.imgur.com/7n7f9.png)](https://i.stack.imgur.com/7n7f9.png)