EDB — 1C0

Exercises

1. [1C0]Let $n,m\ge 1$ be integers, and set

   $$I_{n,m}={\int }_0^1{x}^n(\log x{)}^m\mathbb{d}x:$$

   relate $I_{n,m}$ with $I_{n,m-1}$; use that relation to explicitly calculate

   $${\int }_0^1{x}^n(\log x{)}^n\mathbb{d}x.$$
   Solution 1

   [1C1]↺↻