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so here what i want to integrate

$$ r(x)= \frac{n!}{(x(x + 1).....(x + n))} $$ and here what i have done, i will thankful for tips

i have started with partial fractions $$ r(x) = \frac{A_0}{x} + \frac{A_1}{x+1}+\frac{A_2}{x+2} + ... +\frac{A_n}{x+n} $$

then i get $$ n! = A_0(x+1)(x+2)...(x+n)+A_1 x(x+2)...(x+n) + A_2 x(x+1)(x+3)...(x+n) + ... + A_n x(x+1)(x+2)...(x+n-1) $$ here were i stuck and i don't know how to continue, how to find the value of A so i could easliy then integrate the function

asd asdd
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    This should help: https://math.stackexchange.com/q/1912720/42969 – found with Approach0 – Martin R Mar 26 '23 at 17:22
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    You could try the partial fractions with $n=1,2,3$ and see if you spot a pattern – Henry Mar 26 '23 at 17:23
  • @MartinR i have seen the link, but it get more complicated, first of all, if i used the fromula, before using it i will need to prove it , shich doens't really help, and secondly this might be me but i get more lost and don't know how it could help me. if possible could you explain more – asd asdd Mar 26 '23 at 21:26

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