Can anyone show me how to integrate:

[(n+1)*(x^n)]*[1+x+(x^(x+1))+(x^(x+1)^(x+2))+(x^(x+1)^(x+2)^(x+3) )] over [0,1]?


I know I'm supposed to do it twice but I'm not sure what to take as u and dv (I'm assuming I should take the big messy one as u and the first nicer one as dv, but even still I'm having trouble).

Edit: Integrate with respect to x (not n, but I guess that's obvious).