`int_0^1x(1-x)^ndx`

Explanation

`I=int_0^1x(1-x)^ndx`
=`int_0^1(1-x)x^ndx`
=`int(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))`