Question 1141106
Use a substitution,
{{{u=x+1}}}
{{{x=u-1}}}
So,
{{{int(x(1+x)^5,dx)=int((u-1)u^5,du)}}}
{{{int(x(1+x)^5,dx)=int((u^6-u^5),du)}}}
{{{int(x(1+x)^5,dx)=u^7/7-u^6/6+C}}}
{{{int(x(1+x)^5,dx)=(x+1)^7/7-(x+1)^6/6+C}}}
Now simplify.