EDB — 1C0

Exercises

1. [1C0]Let \(n,m≥ 1\) be integers, and set

   \[ I_{n,m} = ∫_ 0^ 1 x^ n (\log x)^ m\, {\mathbb {d}}x\quad : \]

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

   \[ ∫_ 0^ 1 x^ n (\log x) ^ n\, {\mathbb {d}}x~ . \]
   Solution 1

   [1C1]↺↻