Formula for Area of a Triangle - nodal basis function

Question

Let T be a triangle with corners $P_1, P_2, P_3$ and the nodal basis function $\lambda_1, \lambda_2, \lambda_3$ and $\alpha, \beta, \in \mathbb{N}_0$. I want to show that $$ \int_{T}^{} \lambda_1^\alpha\lambda_2^\beta \lambda_3^\gamma dx = 2 |T| \frac{\alpha! \beta!\gamma!}{(2+\alpha+\beta+\gamma)} $$ How do I show this and is this a known formula? If so, for what do we need to know and use this?