for m>0,n>0.show integration ---x(pow)m (1-x)(Pow)n from 0 to 1=

m!n!/(m+n+1)!

Dear yashika

for m>0,n>0

I_m,n=∫x^m(1-x)ⁿ dx  limit 0 to 1

        intigrate by using 1st and 2nd function

       =-1/(n+1)  x^m(1-x)ⁿ⁺¹  limit 0 to 1  +m/(n+1) ∫x^m-1(1-x)ⁿ⁺¹ dx  limit 0 to 1

       =0 +m/(n+1) ∫x^m-1(1-x)(1-x)ⁿ dx  limit 0 to 1

       = m/(n+1) [∫x^m-1(1-x)ⁿ dx - ∫x^m(1-x)ⁿdx ]    limit 0 to 1

       =m/(n+1) [I_{m-1,n  -} I_{m,n   ^]}

simplify     I_m,n   =   m/(m+n+1) I_m-1,n 

                       =m*(m-1)/(m+n+1)(m+n)  I_m-2,n

  repeat this process you will get desire result

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