I am reading Wong's book on "Asymptotic Approximations of Integrals". On page 497, the book recalls (without proof) the following estimate: for all $\delta>0$ and $\nu>1$, $$ \int_\delta^\infty t^m e^{-\nu t^2} dt \le K_\delta e^{-\nu \delta^2}, $$ where $K_\delta$ is a constant independent of $\nu$.
May I know whether the above estimate is a well-known result? Could you provide a reference for it?