So your integral is equal to `1/(n+1)^2` which is less than `1/(n+1)` because n is a natural number.
I'm sorry because the above formula is hard to read. You should've posted this as a question under math.
Given I = Integral x^n/(x+1) demonstrate that I <= 1/(n+1). The limits of integration are x=0 to x=1 and n is natural number.