Let-consider-K-0-1-1-x-a-1-x-b-1-x-c-x-1-lnx-dx-prove-that-e-K-a-b-a-c-b-c-a-b-c-a-b-c-

Question Number 69241 by ~ À ® @ 237 ~ last updated on 21/Sep/19

L e t c o n s i d e r K = \int_{0}^{1} \frac{(1 - x^{a}) (1 - x^{b}) (1 - x^{c})}{(x - 1) l n x} d x

p r o v e t h a t

e^{K} = \frac{(a + b)! (a + c)! (b + c)!}{a! b! c! (a + b + c)!}