Using properties evaluate the following definite integrals, evaluate the following: `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`
=`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) = `((n+2)-(n+1))/((n+1)(n+2))`
`1/((n+1)(n+2))`