# Cauchy's Formula for Repeated Integration

Repeated integrations can come up pretty often. It's a bit of a pain but the OG has formula for this. Proof is via [induction](https://en.wikipedia.org/wiki/Cauchy_formula_for_repeated_integration). 

$$
*n\int*{a}^{t} f(x) d x^{n}=\frac{1}{(n-1) !} \int\_{a}^{t}(t-x)^{n-1} f(x) d x
$$