`int_(0)^(1)x(1-x)^(n)dx`

Explanation

`int_(0)^(1)x(1-x)^(n)dx`
`=int_(0)^(1)(1-x).{1-(1-x)}^(n)dx`
[ प्रगुण (4 ) से ]
`=int_(0)^(1)(1-x).x^(n)dx`
`=int_(0)^(1)(x(n)-x^(n+1))dx`
`=[(x^(n+1))/(n+1)-(x^(n+2))/(n+2)]_(0)^(1)`
`=(1)/(n+1)-(1)(n+2)=(1)/((n+1)(n+2))`