Closed expressions for ∫¹₀𝑡⁻¹𝑙𝑜𝑔ⁿ⁻¹𝑡log^{𝑝}(1-𝑡)𝑑𝑡

Abstract

Closed expressions for the integral ∫ 0 1 t − 1 log n − 1 t log p ( 1 − t ) d t \smallint _0^1{t^{ - 1}}{\log ^{n - 1}}t{\log ^p}(1 - t)\;dt , whose general form is given elsewhere, are listed for n = 1 ( 1 ) 9 n = 1(1)9 , p = 1 ( 1 ) 9 p = 1(1)9 . A formula is derived which allows an easy evaluation of these expressions by formula manipulation on a computer.