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)!))


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

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