Mr F says: u = 1 + e^x => du/dx = e^x => dx = du/e^x. So the integral becomes int e^x sqrt(u) du/e^x = int sqrt(u) du.
and
int((x^2)(e^x))
Mr F says: Use integration by parts TWICE. First time will leave you with an integral of the form int x e^x dx. Second time leaves you with an integral of the form int e^x dx.