# Feynmann's Trick For Exponential Integrals

## Table of Contents

## Feynmann’s Trick For Exponential Integrals #

$$\int_0^{\infty} x^n e^{-tx} dx = \frac{n!}{t^{n+1}}$$

Where

- \(t\) is a constant, and
- \(n!\) is the Gamma function (does not require \(n\) to be an integer)

Feynmann’s trick involves “differentiating under the integral” which is a whole technique on its own, and the above formula is something that can be found using this technique. I found that formula particularly hard to find online, so I decided to write it up.